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This paper will explore the design and implementation of quantum networks in space integrated with quantum networks on Earth. We propose a three-layer approach, involving GEO and LEO satellites integrated with terrestrial ground stations. We first analyze the channel conditions between the three layers, and then highlight the key role of LEO satellites in the integrated space-terrestrial system - namely the source of entanglement distribution between specified terrestrial stations via direct downlink quantum-optical channels. The GEO satellites in the considered system are used primarily as coordination stations, managing and directing the LEO satellites regarding the positioning and timing of entanglement distribution. Complexity, in the form of entanglement distillation and quantum-state correction, is concentrated at the terrestrial stations, and teleportation is used as the primary quantum channel in the LEO uplinks and the inter-terrestrial channels. Although our designs are futuristic in that they assume limited quantum memory at the transceivers, we also discuss some near-term uses of our network in which no quantum memory is available., Comment: Published: IEEE Communications Magazine

Due to the numerous limitations of current quantum devices, quantum error mitigation methods become potential solutions for realizing practical quantum applications in the near term. Zero-Noise Extrapolation (ZNE) and Clifford Data Regression (CDR) are two promising quantum error mitigation methods. Based on the characteristics of these two methods, we propose a new method named extrapolated CDR (eCDR). To benchmark our method, we embed eCDR into a quantum application, specifically multi-layer quantum routing. Quantum routers direct a quantum signal from one input path to a quantum superposition of multiple output paths and are considered important elements of future quantum networks. Multi-layer quantum routers extend the scalability of quantum networks by allowing for further superposition of paths. We benchmark the performance of multi-layer quantum routers implemented on current superconducting quantum devices instantiated with the ZNE, CDR, and eCDR methods. Our experimental results show that the new eCDR method significantly outperforms ZNE and CDR for the 2-layer quantum router. Our work highlights how new mitigation methods built from different components of pre-existing methods, and designed with a core application in mind, can lead to significant performance enhancements.

Despite being an integral part of the vision of quantum Internet, Earth-to-satellite (uplink) quantum communications have been considered more challenging than their satellite-to-Earth (downlink) counterparts due to the severe channel-loss fluctuations (fading) induced by atmospheric turbulence. The question of how to address the negative impact of fading on Earth-to-satellite quantum communications remains largely an open issue. In this work, we explore the feasibility of exploiting spatial diversity as a means of fading mitigation in Earth-to-satellite Continuous-Variable (CV) quantum-classical optical communications. We demonstrate, via both our theoretical analyses of quantum-state evolution and our detailed numerical simulations of uplink optical channels, that the use of spatial diversity can improve the effectiveness of entanglement distribution through the use of multiple transmitting ground stations and a single satellite with multiple receiving apertures. We further show that the transfer of both large (classically-encoded) and small (quantum-modulated) coherent states can benefit from the use of diversity over fading channels. Our work represents the first quantitative investigation into the use of spatial diversity for satellite-based quantum communications in the uplink direction, showing under what circumstances this fading-mitigation paradigm, which has been widely adopted in classical communications, can be helpful within the context of Earth-to-satellite CV quantum communications., Comment: 18 pages, 7 figures. Comments are welcome

The next generation of space-based networks will contain optical clocks embedded within satellites. To fully realize the capabilities of such clocks, high-precision clock synchronization across the networks will be necessary. Current experiments have shown the potential for classical frequency combs to synchronize remote optical clocks over free-space. However, these classical combs are restricted in precision to the standard quantum limit. Quantum frequency combs, however, which exhibit quantum properties such as squeezing and entanglement, provide pathways for going beyond the standard quantum limit. Here, we present our perspective on the prospects for practical clock synchronization in space using both classical and quantum frequency combs. We detail the current outcomes achievable with a classical frequency comb approach to synchronization, before quantifying the potential outcomes offered by quantum frequency combs. Challenges to be overcome in deploying frequency combs in space are presented, and the implications of almost-perfect synchronization for future space-based applications and experiments discussed., Comment: 23 pages, 11 figures, perspective, comments welcome

Classical free-space optical (FSO) communication promises massive data throughput rates relative to traditional wireless technologies - an attractive outcome now being pursued in the context of satellite-ground, inter-satellite and deep-space communications. The question we investigate here is: how can we minimally alter classical FSO systems, both in infrastructure and in energy input, to provide some element of quantum communication coexisting with classical communications? To address this question, we explore additional Gaussian displacements to classical FSO encoding on the satellite, determining the minimum signal requirements that will meet given specifications on the combined classical and quantum communications throughput. We then investigate whether enhanced quantum-based amplifiers embedded in receivers, which have proven advantageous in standalone quantum communication, can enhance our combined classical-quantum communication throughput. We show how this is indeed the case, but only at the cost of some additional receiver complexity, relative to standalone quantum communications. This additional complexity takes the form of an additional beamsplitter and two heterodyne detectors at the receiver. Our results illustrate a viable pathway to realising quantum communication from classical FSO systems with minimal design changes., Comment: 10 pages, 5 figures. Accepted for publication in IEEE QCNC 2024 conference proceedings

In typical laser communications classical information is encoded by modulating the amplitude of the laser beam and measured via direct detection. We add a layer of security using quantum physics to this standard scheme, applicable to free-space channels. We consider a simultaneous classical-quantum communication scheme where the classical information is encoded in the usual way and the quantum information is encoded as fluctuations of a sub-Poissonian noise-floor. For secret key generation, we consider a continuous-variable quantum key distribution protocol (CVQKD) using a Gaussian ensemble of squeezed states and direct detection. Under the assumption of passive attacks secure key generation and classical communication can proceed simultaneously. Compared with standard CVQKD. which is secure against unrestricted attacks, our added layer of quantum security is simple to implement, robust and does not affect classical data rates. We perform detailed simulations of the performance of the protocol for a free-space atmospheric channel. We analyse security of the CVQKD protocol in the composable finite-size regime.

As an alternative to quantum error correction, quantum error mitigation methods, including Zero-Noise Extrapolation (ZNE), have been proposed to alleviate run-time errors in current noisy quantum devices. In this work, we propose a modified version of ZNE that provides for a significant performance enhancement on current noisy devices. Our modified ZNE method extrapolates to zero-noise data by evaluating groups of noisy data obtained from noise-scaled circuits and selecting extrapolation functions for each group with the assistance of estimated noisy simulation results. To quantify enhancement in a real-world quantum application, we embed our modified ZNE in Quantum Random Access Memory (QRAM) - a memory system important for future quantum networks and computers. Our new ZNE-enhanced QRAM designs are experimentally implemented on a 27-qubit noisy superconducting quantum device, the results of which demonstrate QRAM fidelity can be improved significantly relative to traditional ZNE usage. Our results demonstrate the critical role the extrapolation function plays in ZNE - judicious choice of that function on a per-measurement basis can make the difference between a quantum application being functional or non-functional.

We explore the relationship between the Poisson deformation theory, birational geometry, and Springer theory of crepant partial resolutions of conical affine symplectic singularities. We show that given any crepant partial resolution $X'$, the Poisson deformation functor of $X'$ is prorepresentable and unobstructed. Additionally, we define a version of the Namikawa Weyl group $W_{X'}$ for partial resolutions, such that $W_{X'}$ is a parabolic subgroup of the Namikawa Weyl group $W_X$ determined by the birational geometry of $X'$, in particular by a face of a relative movable cone. If $Y$ is a Q-factorial terminalization which covers $X'$, we show there is a natural morphism from Poisson deformations of $Y$ to those of $X'$, and that this morphism is a Galois covering with Galois group $W_{X'}$, building on work of Namikawa. Finally, we put these partial resolutions and their universal deformations into the context of work of McGerty and Nevins, obtaining some preliminary results concerning their Springer theory., Comment: 52 pages. Minor updates

Quantum super-resolution involves resolving two sources below the Rayleigh limit using quantum optics. Such a technique would allow high-precision inter-satellite positioning and tracking on communication and navigation constellations. Due to the size, weight and power constraints typical of low-earth-orbit (LEO) satellites, a simple solution is often preferred. Here, we show that a balanced homodyne detection (BHD) setup using a shaped single-mode local oscillator can achieve super-resolution despite typical photonic losses. We further analyze the impact of a fluctuating and fixed centroid misalignment due to satellite pointing issues, and find that fixed misalignment is comparatively more detrimental to the performance of a BHD setup. Thus, our study provides a practical assessment of BHD to achieve super-resolution on a modern LEO satellite platform. Finally, we discuss how our analysis can be extended to stellar sources for astronomical applications., Comment: 9 pages, 5 figures, comments welcome

Precision navigation and timing, very-long-baseline interferometry, next-generation communication, sensing, and tests of fundamental physics all require a highly synchronized network of clocks. With the advance of highly-accurate optical atomic clocks, the precision requirements for synchronization are reaching the limits of classical physics (i.e. the standard quantum limit, SQL). Efficiently overcoming the SQL to reach the fundamental Heisenberg limit can be achieved via the use of squeezed or entangled light. Although approaches to the Heisenberg limit are well understood in theory, a practical implementation, such as in space-based platforms, requires that the advantage outweighs the added costs and complexity. Here, we focus on the question: can entanglement yield a quantum advantage in clock synchronization over lossy satellite-to-satellite channels? We answer in the affirmative, showing that the redundancy afforded by the two-mode nature of entanglement allows recoverability even over asymmetrically lossy channels. We further show this recoverability is an improvement over single-mode squeezing sensing, thereby illustrating a new complexity-performance trade-off for space-based sensing applications., Comment: 6 pages, 4 figures, comments welcome

Coherent measurement of quantum signals used for continuous-variable (CV) quantum key distribution (QKD) across satellite-to-ground channels requires compensation of phase wavefront distortions caused by atmospheric turbulence. One compensation technique involves multiplexing classical reference pulses (RPs) and the quantum signal, with direct phase measurements on the RPs then used to modulate a real local oscillator (RLO) on the ground - a solution that also removes some known attacks on CV-QKD. However, this is a cumbersome task in practice - requiring substantial complexity in equipment requirements and deployment. As an alternative to this traditional practice, here we introduce a new method for estimating phase corrections for an RLO by using only intensity measurements from RPs as input to a convolutional neural network, mitigating completely the necessity to measure phase wavefronts directly. Conventional wisdom dictates such an approach would likely be fruitless. However, we show that the phase correction accuracy needed to provide for non-zero secure key rates through satellite-to-ground channels is achieved by our intensity-only measurements. Our work shows, for the first time, how artificial intelligence algorithms can replace phase-measuring equipment in the context of CV-QKD delivered from space, thereby delivering an alternate deployment paradigm for this global quantum-communication application.

With sub-threshold quantum error correction on quantum hardware still out of reach, quantum error mitigation methods are currently deemed an attractive option for implementing certain applications on near-term noisy quantum devices. One such application is quantum routing - the ability to map an incoming quantum signal into a superposition of paths. In this work, we use a 7-qubit IBM quantum device to experimentally deploy two promising quantum error mitigation methods, Zero-Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC), in the context of quantum routing. Importantly, beyond investigating the improved performance of quantum routing via ZNE and PEC separately, we also investigate the routing performance provided by the concatenation of these two error-mitigation methods. Our experimental results demonstrate that such concatenation leads a very significant performance improvement relative to implementation with no error mitigation. Indeed, an almost perfect performance in terms of fidelity of the output entangled paths is found. These new results reveal that with concatenated quantum error-mitigation embedded, useful quantum routing becomes feasible on current devices without the need for quantum error correction - opening up a potential implementation pathway to other applications that utilize a superposition of communication links.

Due to turbulence and tracking errors, free-space optical channels involving mobile transceivers are characterized by a signal's partial loss or complete erasure. This work presents an error correction protocol capable of protecting a signal passing through such channels by encoding it with an ancillary entangled bipartite state. Beyond its ability to offer protection under realistic channel conditions, novel to our protocol is its ability to encompass both classical and quantum information on the encoded signal. We show how, relative to non-encoded direct transmission, the protocol can improve the fidelity of transmitted coherent states over a wide range of losses and erasure probabilities. In addition, the use of ancillary non-Gaussian entangled bipartite states in the signal encoding is considered, showing how this can increase performance. Finally, we briefly discuss the application of our protocol to the transmission of more complex input states, such as multi-mode entangled states.

Quantum Key Distribution (QKD) is considered the most immediate application to be widely implemented amongst a variety of potential quantum technologies. QKD enables sharing secret keys between distant users, using photons as information carriers. An ongoing endeavour is to implement these protocols in practice in a robust, and compact manner so as to be efficiently deployable in a range of real-world scenarios. Single Photon Sources (SPS) in solid-state materials are prime candidates in this respect. Here, we demonstrate a room temperature, discrete-variable quantum key distribution system using a bright single photon source in hexagonal-boron nitride, operating in free-space. Employing an easily interchangeable photon source system, we have generated keys with one million bits length, and demonstrated a secret key of approximately 70,000 bits, at a quantum bit error rate of 6%, with $\varepsilon$-security of $10^{-10}$. Our work demonstrates the first proof of concept finite-key BB84 QKD system realised with hBN defects.

Quantum routing, the entanglement of an input quantum signal over multiple output paths, will be an important aspect of future quantum networks. Implementation of such routing in emerging quantum networks via the noisy quantum devices currently under development is a distinct possibility. Quantum error correction, suitable for the arbitrary noisy quantum channels experienced in the routing process, will be required. In this work, we design a combined circuit for quantum routing and quantum error correction, and carry out the first implementation of such a circuit on a noisy real-world quantum device. Under the assumption of statistical knowledge on the channel, we experimentally verify the quantum nature of the error-corrected quantum routing by determining the path-entanglement through quantum state tomography, measuring also its probability of success. The quantum error correction deployed is identified as successful in terms of improving the routing. Our experiments validate, for the first time, that error-corrected quantum routing in near-term noisy quantum-computing devices is feasible, and our detailed results provide a quantum-routing benchmark for all near-term quantum hardware.

Quantum states of light being transmitted via realistic free-space channels often suffer erasure errors due to several factors such as coupling inefficiencies between transmitter and receiver. In this work, an error correction code capable of protecting a single-mode quantum state against erasures is presented. Our three-mode code protects a single-mode Continuous Variable (CV) state via a bipartite CV entangled state. In realistic deployments, it can almost completely reverse a single erasure on the encoded state, and for two erasures can it improve the fidelities of received states relative to direct transmission. The bipartite entangled state used in the encoding can be Gaussian or non-Gaussian, with the latter further enhancing the performance of the code. Our new code is the simplest code known that protects a single mode against erasures and should prove useful in the construction of practical CV quantum networks that rely on free-space optics., Comment: Accepted for publication in IEEE GLOBECOM 2022

Hybrid entanglement between discrete-variable (DV) and continuous-variable (CV) quantum systems is an essential resource for heterogeneous quantum networks. Our previous work showed that in lossy channels the teleportation of DV qubits, via CV-entangled states, can be significantly improved by a new protocol defined by a modified Bell state measurement at the sender. This work explores whether a new, similarly modified, CV-based teleportation protocol can lead to improvement in the transfer of hybrid entangled states. To set the scene, we first determine the performance of such a modified protocol in teleporting CV-only qubits, showing that significant improvement over traditional CV-based teleportation is obtained. We then explore similar modifications in the teleportation of a specific hybrid entangled state showing that significant improvement over traditional CV-based teleportation is again found. For a given channel loss, we find teleporting the DV qubit of the hybrid entangled state can always achieve higher fidelity than teleporting the CV qubit. We then explore the use of various non-Gaussian operations in our modified teleportation protocol, finding that, at a cost of lower success probability, quantum scissors provides the most improvement in the loss tolerance. Our new results emphasize that in lossy conditions, the quantum measurements undertaken at the sender can have a surprising and dramatic impact on CV-based teleportation., Comment: 9 pages, 9 figures

The Continuous-Variable (CV) quantum state of light allows for the teleportation of a Discrete-Variable (DV) photonic qubit. Such an operation is useful in the realm of hybrid quantum networks. However, it is known that the teleportation of a DV qubit via a Gaussian CV resource channel is severely limited under channel loss, with a teleportation fidelity beyond the classical limit unattainable for losses exceeding a small threshold of 0.5 dB. In this work, we present a new non-deterministic teleportation protocol that combines a Gaussian CV resource channel with a modified form of the Bell State Measurement that accommodates a DV-qubit fidelity beyond the classical limit for channel losses up to 20~dB. Beyond this orders of magnitude improvement, we also show how the use of non-Gaussian operations on the CV resource channel can lead to a DV-qubit fidelity approaching unity for any channel loss., Comment: 11 pages

High-purity single photon sources (SPS) that can operate at room temperature are highly desirable for a myriad of applications, including quantum photonics and quantum key distribution. In this work, we realise an ultra-bright solid-state SPS based on an atomic defect in hexagonal boron nitride (hBN) integrated with a solid immersion lens (SIL). The SIL increases the source efficiency by a factor of six, and the integrated system is capable of producing over ten million single photons per second at room temperature. Our results are promising for practical applications of SPS in quantum communication protocols.

Continuous Variable (CV) non-Gaussian resources are fundamental in the realization of quantum error correction for CV-based quantum communications and CV-based computing. In this work, we investigate the use of CV non-Gaussian states as quantum teleportation resource states in the context of the transmission of coherent and squeezed states through noisy channels. We consider an array of different non-Gaussian resource states, and compute the fidelity of state teleportation achieved for each resource. Our results show that the use of non-Gaussian states presents a significant advantage compared to the traditional resource adopted for CV teleportation; the Gaussian two-mode squeezed vacuum state. In fiber-based quantum communications, the range of quantum teleportation is increased by approximately 40% via the use of certain non-Gaussian states. In satellite-to-ground quantum communications, for aperture configurations consistent with the Micius satellite, the viable range of quantum teleportation is increased from 700 km to over 1200 km. These results represent a significant increase in the performance of pragmatic and realizable quantum communications in both terrestrial and space-based networks., Comment: Accepted for publication in 2021 IEEE GLOBECOM

Quantum technology is exploding. Computing, communication, and sensing are just a few areas likely to see breakthroughs in the next few years. Worldwide, national governments, industries, and universities are moving to create a new class of workforce - the Quantum Engineers. Demand for such engineers is predicted to be in the tens of thousands within a five-year timescale. However, how best to train this next generation of engineers is far from obvious. Quantum mechanics - long a pillar of traditional physics undergraduate degrees - must now be merged with traditional engineering offerings. This paper discusses the history, development, and first year of operation of the world's first undergraduate degree in quantum engineering. The main purpose of the paper is to inform the wider debate, now being held by many institutions worldwide, on how best to formally educate the Quantum Engineer., Comment: Comments welcome

Designing a practical Continuous Variable (CV) Quantum Key Distribution (QKD) system requires an estimation of the quantum channel characteristics and the extraction of secure key bits based on a large number of distributed quantum signals. Meeting this requirement in short timescales is difficult. On standard processors, it can take several hours to reconcile the required number of quantum signals. This problem is exacerbated in the context of Low Earth Orbit (LEO) satellite CV-QKD, in which the satellite flyover time is constrained to be less than a few minutes. A potential solution to this problem is massive parallelisation of the classical reconciliation process in which a large-code block is subdivided into many shorter blocks for individual decoding. However, the penalty of this procedure on the important final secured key rate is non-trivial to determine and hitherto has not been formally analysed. Ideally, a determination of the optimal reduced block size, maximising the final key rate, would be forthcoming in such an analysis. In this work, we fill this important knowledge gap via detailed analyses and experimental verification of a CV-QKD sliced reconciliation protocol that uses large block-length low-density parity-check decoders. Our new solution results in a significant increase in the final key rate relative to non-optimised reconciliation. In addition, it allows for the acquisition of quantum secured messages between terrestrial stations and LEO satellites within a flyover timescale even using off-the-shelf processors. Our work points the way to optimised global quantum networks secured via fundamental physics., Comment: Updated References

The photonic Temporal Mode (TM) represents a possible candidate for the delivery of viable multidimensional quantum communications. However, relative to other multidimensional quantum information carriers such as the Orbital Angular Momentum (OAM), the TM has received less attention. Moreover, in the context of the emerging quantum internet and satellite-based quantum communications, the TM has received no attention. In this work, we remedy this situation by considering the traversal through the satellite-to-Earth channel of single photons encoded in TM space. Our results indicate that for anticipated atmospheric conditions the photonic TM offers a promising avenue for the delivery of high-throughput quantum communications from a satellite to a terrestrial receiver. In particular, we show how these modes can provide for improved multiplexing performance and superior quantum key distribution in the satellite-to-Earth channel, relative to OAM single-photon states. The levels of TM discrimination that guarantee this outcome are outlined and implications of our results for the emerging satellite-based quantum internet are discussed., Comment: 7 pages, 3 figures. Comments are welcome

In developing the global Quantum Internet, quantum communication with low-Earth-orbit satellites will play a pivotal role. Such communication will need to be two way: effective not only in the satellite-to-ground (downlink) channel but also in the ground-to-satellite channel (uplink). Given that losses on this latter channel are significantly larger relative to the former, techniques that can exploit the superior downlink to enhance quantum communication in the uplink should be explored. In this work we do just that - exploring how continuous variable entanglement in the form of two-mode squeezed vacuum (TMSV) states can be used to significantly enhance the fidelity of ground-to-satellite quantum-state transfer relative to direct uplink-transfer. More specifically, through detailed phase-screen simulations of beam evolution through turbulent atmospheres in both the downlink and uplink channels, we demonstrate how a TMSV teleportation channel created by the satellite can be used to dramatically improve the fidelity of uplink coherent-state transfer relative to direct transfer. We then show how this, in turn, leads to the uplink-transmission of a higher alphabet of coherent states. Additionally, we show how non-Gaussian operations acting on the received component of the TMSV state at the ground station can lead to even further enhancement. Since TMSV states can be readily produced in situ on a satellite platform and form a reliable teleportation channel for most quantum states, our work suggests future satellites forming part of the emerging Quantum Internet should be designed with uplink-communication via TMSV teleportation in mind.

Heterogeneous quantum networks consisting of mixed-technologies - Continuous Variable (CV) and Discrete Variable (DV) - will become ubiquitous as global quantum communication matures. Hybrid quantum-entanglement between CV and DV modes will be a critical resource in such networks. A leading candidate for such hybrid quantum entanglement is that between Schr\"odinger-cat states and photon-number states. In this work, we explore the use of Two-Mode Squeezed Vacuum (TMSV) states, distributed from satellites, as a teleportation resource for the re-distribution of our candidate hybrid entanglement pre-stored within terrestrial quantum networks. We determine the loss conditions under which teleportation via the TMSV resource outperforms direct-satellite distribution of the hybrid entanglement, in addition to quantifying the advantage of teleporting the DV mode relative to the CV mode. Our detailed calculations show that under the loss conditions anticipated from Low-Earth-Orbit, DV teleportation via the TMSV resource will always provide for significantly improved outcomes, relative to other means for distributing hybrid entanglement within heterogeneous quantum networks., Comment: 15 pages; updated references and minor clarifications

Continuous variable quantum key distribution (CV-QKD) offers information-theoretic secure key sharing between two parties. The sharing of a phase reference frame is an essential requirement for coherent detection in CV-QKD. Due to the potential attacks related to transmitting the local oscillator (LO) alongside quantum signals, there has been a focus on using local LOs (LLOs) to establish a shared phase reference. In this work, we develop a new noise model of a current state-of-the-art LLO scheme in the context of the satellite-to-Earth channel. In doing this, we encapsulate detailed phase-screen calculations that determine the coherent efficiency - a critical parameter in free-space CV-QKD that characterizes the wavefront aberrations caused by atmospheric turbulence. Using our new noise model we then determine the CV-QKD key rates for the satellite-to-Earth channel, secure under general attacks in the finite-size regime of the LLO scheme. Our results are of practical importance for next-generation quantum-enabled satellites that utilize multi-photon technology as opposed to single-photon technology.

Artificial Intelligence (AI) solutions for wireless location estimation are likely to prevail in many real-world scenarios. In this work, we demonstrate for the first time how the Cramer-Rao upper bound on localization accuracy can facilitate efficient neural-network solutions for wireless location estimation. In particular, we demonstrate how the number of neurons for the network can be intelligently chosen, leading to AI location solutions that are not time-consuming to run and less likely to be plagued by over-fitting. Experimental verification of our approach is provided. Our new algorithms are directly applicable to location estimates in many scenarios including the Internet of Things, and vehicular networks where vehicular GPS coordinates are unreliable or need verifying. Our work represents the first successful AI solution for a communication problem whose neural-network design is based on fundamental information-theoretic constructs. We anticipate our approach will be useful for a wide range of communication problems beyond location estimation., Comment: This work has been submitted to the IEEE for possible publication

Anonymity networks are becoming increasingly popular in today's online world as more users attempt to safeguard their online privacy. Tor is currently the most popular anonymity network in use and provides anonymity to both users and services (hidden services). However, the anonymity provided by Tor is also being misused in various ways. Hosting illegal sites for selling drugs, hosting command and control servers for botnets, and distributing censored content are but a few such examples. As a result, various parties, including governments and law enforcement agencies, are interested in attacks that assist in de-anonymising the Tor network, disrupting its operations, and bypassing its censorship circumvention mechanisms. In this survey paper, we review known Tor attacks and identify current techniques for the de-anonymisation of Tor users and hidden services. We discuss these techniques and analyse the practicality of their execution method. We conclude by discussing improvements to the Tor framework that help prevent the surveyed de-anonymisation attacks., Comment: This work is published in IEEE Communications Surveys & Tutorials and is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/. Link to the article https://ieeexplore.ieee.org/abstract/document/9471821

The entanglement structure between different frequency components within broadband quantum light pulses, forged at entanglement creation, represents a promising route to the practical delivery of many multipartite quantum information applications. However, the scalability of such applications is largely limited by the entanglement decoherence caused by photon loss. One promising method to combat such losses is noiseless linear amplification. However, while there have been various procedures that implement noiseless linear amplification on single-mode states, no realization has thus far been proposed for noiseless linear amplification on quantum states carrying a multimode structure. In this work we close this gap, proposing a novel Noiseless Linear Amplifier (NLA) with Photon Catalysis (PC), namely, the PC-NLA. Constructing a multimode version of an existing NLA that uses Quantum Scissors (QS), the QS-NLA, we then show how the PC-NLA is compatible with the QS-NLA, even though the former uses half the physical resources of the latter. We then apply our newly developed multimode NLA frameworks to the problem of Continuous-Variable (CV) entanglement distillation, determining how the multimode structure of the entanglement impacts the performance of the NLAs. Different from single-mode NLA analyses, we find that a multimode NLA is only effective as a CV entanglement distillation strategy when the channel loss is beyond some threshold - a threshold largely dependent on the multimode structure. The results provided here will be valuable for real-world implementations of multipartite quantum information applications that utilize complex entanglement structure within broadband light pulses., Comment: 10 pages, 7 figures

In this work, we explore the feasibility of performing satellite-to-Earth quantum key distribution (QKD) using the orbital angular momentum (OAM) of light. Due to the fragility of OAM states the conventional wisdom is that turbulence would render OAM-QKD non-viable in a satellite-to-Earth channel. However, based on detailed phase screen simulations of the anticipated atmospheric turbulence we find that OAM-QKD is viable in some system configurations, especially if quantum channel information is utilized in the processing of post-selected states. More specifically, using classically entangled light as a probe of the quantum channel, and reasonably-sized transmitter-receiver apertures, we find that non-zero QKD rates are achievable on sea-level ground stations. Without using classical light probes, OAM-QKD is relegated to high-altitude ground stations with large receiver apertures. Our work represents the first quantitative assessment of the performance of OAM-QKD from satellites, showing under what circumstances the much-touted higher dimensionality of OAM can be utilized in the context of secure communications., Comment: 15 pages, 8 figures. Manuscript improved (mainly some symbol changes) for better clarity. Comments are welcome

The recent outbreak of COVID-19 has taken the world by surprise, forcing lockdowns and straining public health care systems. COVID-19 is known to be a highly infectious virus, and infected individuals do not initially exhibit symptoms, while some remain asymptomatic. Thus, a non-negligible fraction of the population can, at any given time, be a hidden source of transmissions. In response, many governments have shown great interest in smartphone contact tracing apps that help automate the difficult task of tracing all recent contacts of newly identified infected individuals. However, tracing apps have generated much discussion around their key attributes, including system architecture, data management, privacy, security, proximity estimation, and attack vulnerability. In this article, we provide the first comprehensive review of these much-discussed tracing app attributes. We also present an overview of many proposed tracing app examples, some of which have been deployed countrywide, and discuss the concerns users have reported regarding their usage. We close by outlining potential research directions for next-generation app design, which would facilitate improved tracing and security performance, as well as wide adoption by the population at large., Comment: Paper has been accepted for publication in IEEE Access. Currently available on IEEE ACCESS early access (see DOI)

In this work we study the use of noiseless attenuation and noiseless amplification, in terms of multi-mode Continuous-Variable (CV) Quantum Key Distribution (QKD) over satellite-to-ground channels. We propose an improved multi-mode CV-QKD protocol where noiseless attenuation and noiseless amplification operations are applied at the transmitter and the receiver, respectively. Our results show that consistent with single-mode CV-QKD, the noiseless amplification operation, when applied at the receiver, can increase the transmission distance and the channel noise tolerance of multi-mode CV-QKD. Different from single-mode CV-QKD, in multi-mode CV-QKD the key rate improvement offered by noiseless amplification can be further enhanced by adding noiseless attenuation at the transmitter.

Currently, quantum key distribution (QKD) using continuous variable (CV) technology has only been demonstrated over short-range terrestrial links. Here we attempt to answer whether CV-QKD over the much longer satellite-to-Earth channel is feasible. To this end, we first review the concepts and technologies that will enable CV-QKD over the satellite-to-Earth channels. We then consider, in the infinite key limit, the simplest-to-deploy QKD protocols, the coherent state (CS) QKD protocol with homodyne detection and the CS-QKD protocol with heterodyne detection. We then focus on the CS-QKD protocol with heterodyne detection in the pragmatic setting of finite keys, where complete security against general attacks is known. We pay particular attention to the relevant noise terms in the satellite-to-Earth channel and their impact on the secret key rates. In system set-ups where diffraction dominates losses, we find that the main components of the total excess noise are the intensity fluctuations due to scintillation, and the time-of-arrival fluctuations between signal and local oscillator. We conclude that for a wide range of pragmatic system models, CS-QKD with information-theoretic security in the satellite-to-Earth channel is feasible., Comment: 16 pages, 6 figures, 4 tables, Closest to Published Version

Satellite-based quantum cryptography has already been demonstrated using discrete variable technology. Nonetheless, there is great interest in using weak coherent pulses to perform quantum key distribution (QKD) in the continuous variable (CV) paradigm. In this work, we study the feasibility of performing coherent-state CV-QKD via the satellite-to-ground channel. We use numerical methods to simulate atmospheric turbulence and compare the results with ground-based experimental data so as to confirm the validity of our approach. We find the results obtained from the numerical simulations agree well with the experimental data and represent an improvement over the state-of-the-art analytical models. Using the simulation results we then derive QKD key rates and find that useful non-zero key rates can be found over a limited range of zenith angles. Determination of QKD key rates using experimentally validated simulations of low-zenith-angle atmospheric channels represents an important step towards proving the feasibility of real-world satellite-to-Earth CV-QKD.

Non-Gaussian operations have been studied intensively in recent years due to their ability to increase the secret key rate for certain CV-QKD protocols. However, most previous studies on such protocols are carried out in a single-mode setting, even though in reality any quantum state contains multi-mode components in frequency space. In this work we investigate the use of non-Gaussian operations in a multi-mode CV-QKD system. Our main finding is that, contrary to single-mode CV-QKD systems, in generic multi-mode CV-QKD systems it is possible to use non-Gaussian operations to increase the optimized secret key rate. More specifically, we find that at losses of order 30dB, which represents a distance of order 160km and the effective maximum distance for CV-QKD, the key rate for multi-mode non-Gaussian operations can be orders of magnitude higher than single-mode operations. Our results are important for real-world CV-QKD systems especially those dependent on quantum error correction - a process that requires non-Gaussian effects.

The Schr\"odinger's-cat state is created from the macroscopic superposition of coherent states and is well-known to be a useful resource for quantum information processing protocols. In order to extend such protocols to a global scale, we study the continuous variable (CV) teleportation of the cat state via a satellite in low-Earth-orbit. Past studies have shown that the quantum character of the cat state can be preserved after CV teleportation, even when taking into account the detector efficiency. However, the channel transmission loss has not been taken into consideration. Traditionally, optical fibers with fixed attenuation are used as teleportation channels. Our results show that in such a setup, the quantum character of the cat state is lost after 5dB of channel loss. We then investigate the free-space channel between the Earth and a satellite, where the loss is caused by atmospheric turbulence. For a down-link channel of less than 500km and 30dB of loss, we find that the teleported state preserves higher fidelity relative to a fixed attenuation channel. The results in this work will be important for deployments over Earth-Satellite channels of protocols dependent on cat-state qubits., Comment: \c{opyright} 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Hybrid entanglement swapping supports the teleportation of any arbitrary states, regardless of whether the quantum information in the state is encoded in Discrete Variables (DV) or Continuous Variables (CV). In this work, we study the CV teleportation channel created between two ground receivers via direct lossy-distribution from a low-Earth-orbit (LEO) satellite. Such a flexible teleportation protocol has the potential to interconnect a global array of quantum-enabled devices regardless of the different intrinsic technology upon which the devices are built. However, past studies of hybrid entanglement swapping have not accounted for channel transmission loss. Here we derive the general framework for teleporting an arbitrary input mode over a lossy CV teleportation channel. We investigate the specific case where the input modes are part of DV states entangled in the photon number basis, then identify the optimal teleportation strategy. Our results show that, relative to DV photon-number entanglement sourced directly from the satellite, there are circumstances where our teleported DV states retain higher entanglement quality. We discuss the implications of our new results in the context of generating a global network of ultra-secure communications between different quantum-enabled devices which possess line-of-sight connections to LEO satellites. Specifically, we illustrate the impact the teleportation process has on the key rates from a Quantum Key Distribution protocol., Comment: copyright 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Non-Gaussian operations have been studied intensively in recent years due to their ability to enhance the entanglement of quantum states. However, most previous studies on such operations are carried out in a single-mode setting, even though in reality any quantum state contains multi-mode components in frequency space. Whilst there have been general frameworks developed for multi-mode photon subtraction (PS) and photon addition (PA), an important gap exists in that no framework has thus far been developed for multi-mode photon catalysis (PC). In this work we close that gap. We then apply our newly developed PC framework to the problem of continuous variable (CV) entanglement distribution via quantum-enabled satellites. Due to the high pulse rate envisioned for such systems, multi-mode effects will be to the fore in space-based CV deployments. After determining the entanglement distribution possible via multi-mode PC, we then compare our results with the entanglement distribution possible using multi-mode PS and PA. Our results show that multi-mode PC carried out at the transmitter is the superior non-Gaussian operation when the initial squeezing is below some threshold. When carried out at the receiver, multi-mode PC is found to be the superior non-Gaussian operation when the mean channel attenuation is above some threshold. Our new results should prove valuable for next-generation deployments of CV quantum-enabled satellites.

In this work we focus on evaluating the effectiveness of two non-Gaussian operations, photon subtraction (PS) and quantum scissors (QS) in terms of Continuous Variable (CV)-Quantum Key Distribution (QKD) over lossy channels. Each operation is analysed in two scenarios, one with the operation applied transmitter-side to a Two-Mode Squeezed Vacuum (TMSV) state and a second with the operation applied to the TMSV state receiver-side. We numerically evaluate the entanglement and calculate the QKD key rates produced in all four possible scenarios. Our results show that for a fixed value of initial squeezing in the TMSV state, the states produced by the non-Gaussian operations are more robust to loss, being capable of generating higher key rates for a given loss. More specifically, we find that for values of initial TMSV squeezing below 1.5dB the highest key rates are obtained by means of transmitter-QS. On the other hand, for squeezing above 1.5dB we find that receiver-PS produces higher key rates. Our results will be important for future CV-QKD implementations over free-space channels, such as the Earth-satellite channel. Accepted for Publication in Quantum Communications and Information Technology Workshop, IEEE Globecom, HI, USA, December 2019., Comment: Copyright 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Ultra-reliable and low-latency communication (URLLC) is one category of service to be provided by next-generation wireless networks. Motivated by increasing security concerns in such networks, this article focuses on physical layer security (PLS) in the context of URLLC. The PLS technique mainly uses transmission designs based on the intrinsic randomness of the wireless medium to achieve secrecy. As such, PLS is of lower complexity and incurs less latency than traditional cryptography. In this article, we first introduce appropriate performance metrics for evaluating PLS in URLLC, illustrating the tradeoff between latency, reliability, and security. We then identify the key challenging problems for achieving PLS for URLLC, and discuss the role that channel state information can have in providing potential solutions to these problems. Finally, we present our recommendations on future research directions in this emerging area., Comment: 6 pages, 4 figures; Accepted by IEEE Wireless Communications

Satellite-based quantum communications enable a bright future for global-scale information security. However, the spin orbital momentum of light, currently used in many mainstream quantum communication systems, only allows for quantum encoding in a two-dimensional Hilbert space. The orbital angular momentum (OAM) of light, on the other hand, enables quantum encoding in higher-dimensional Hilbert spaces, opening up new opportunities for high-capacity quantum communications. Due to its turbulence-induced decoherence effects, however, the atmospheric channel may limit the practical usage of OAM. In order to determine whether OAM is useful for satellite-based quantum communications, we numerically investigate the detection likelihoods for OAM states that traverse satellite-to-ground channels. We show that the use of OAM through such channels is in fact feasible. We use our new results to then investigate design specifications that could improve OAM detection - particularly the use of advanced adaptive optics techniques. Finally, we discuss how our work provides new insights into future implementations of space-based OAM systems within the context of quantum communications., Comment: 7 pages, 7 figures

Location information will play a very important role in emerging wireless networks such as Intelligent Transportation Systems, 5G, and the Internet of Things. However, wrong location information can result in poor network outcomes. It is therefore critical to verify all location information before further utilization in any network operation. In recent years, a number of information-theoretic Location Verification Systems (LVSs) have been formulated in attempts to optimally verify the location information supplied by network users. Such LVSs, however, are somewhat limited since they rely on knowledge of a number of channel parameters for their operation. To overcome such limitations, in this work we introduce a Machine Learning based LVS (ML-LVS). This new form of LVS can adapt itself to changing environments without knowing the channel parameters. Here, for the first time, we use real-world data to show how our ML-LVS can outperform information-theoretic LVSs. We demonstrate this improved performance within the context of vehicular networks using Received Signal Strength (RSS) measurements at multiple verifying base stations. We also demonstrate the validity of the ML-LVS even in scenarios where a sophisticated adversary optimizes her attack location., Comment: 5 pages, 3 figures

Quantum Key Distribution (QKD) via satellite offers up the possibility of unconditionally secure communications on a global scale. Increasing the secret key rate in such systems, via photonic engineering at the source, is a topic of much ongoing research. In this work we investigate the use of photon-added states and photon-subtracted states, derived from two mode squeezed vacuum states, as examples of such photonic engineering. Specifically, we determine which engineered-photonic state provides for better QKD performance when implemented over channels connecting terrestrial receivers with Low-Earth-Orbit satellites. We quantify the impact the number of photons that are added or subtracted has, and highlight the role played by the adopted model for atmospheric turbulence and loss on the predicted key rates. Our results are presented in terms of the complexity of deployment used, with the simplest deployments ignoring any estimate of the channel, and the more sophisticated deployments involving a feedback loop that is used to optimize the key rate for each channel estimation. The optimal quantum state is identified for each deployment scenario investigated., Comment: Updated reference list

Terahertz (THz) communication is a topic of much research in the context of high-capacity next-generation wireless networks. Quantum communication is also a topic of intensive research, most recently in the context of space-based deployments. In this work we explore the use of THz frequencies as a means to achieve quantum communication within a constellation of micro-satellites in Low-Earth-Orbit (LEO). Quantum communication between the micro-satellite constellation and high-altitude terrestrial stations is also investigated. Our work demonstrates that THz quantum entanglement distribution and THz quantum key distribution are viable deployment options in the micro-satellite context. We discuss how such deployment opens up the possibility for simpler integration of global quantum and wireless networks. The possibility of using THz frequencies for quantum-radar applications in the context of LEO deployments is briefly discussed., Comment: 7 pages, 6 figures

Location information claimed by devices will play an ever-increasing role in future wireless networks such as 5G, the Internet of Things (IoT). Against this background, the verification of such claimed location information will be an issue of growing importance. A formal information-theoretic Location Verification System (LVS) can address this issue to some extent, but such a system usually operates within the limits of idealistic assumptions on a-priori information on the proportion of genuine users in the field. In this work we address this critical limitation by using a Neural Network (NN) showing how such a NN based LVS is capable of efficiently functioning even when the proportion of genuine users is completely unknown a-priori. We demonstrate the improved performance of this new form of LVS based on Time of Arrival measurements from multiple verifying base stations within the context of vehicular networks, quantifying how our NN-LVS outperforms the stand-alone information-theoretic LVS in a range of anticipated real-world conditions. We also show the efficient performance for the NN-LVS when the users' signals have added Non-Line-of-Site (NLoS) bias in them. This new LVS can be applied to a range of location-centric applications within the domain of the IoT., Comment: 6 Pages, 5 figures

Non-Gaussian continuous-variable quantum states represent a pivotal resource in many quantum information protocols. Production of such states can occur through photonic subtraction process either at the transmitter side prior to sending a state through the channel, or at the receiver side on receipt of a state that has traversed the channel. In the context of quantum protocols implemented over communication channels to and from Low-Earth-Orbit (LEO) satellites it is unclear what photonic subtraction set-up will provide for the best performance. In this work we show that for a popular version of continuous-variable Quantum Key Distribution between terrestrial stations and LEO satellites, photon subtraction at the transmitter side is the preferred set-up. Such a result is opposite to that found for fiber-based implementations. Our results have implications for all future space-based missions that seek to take advantage of the opportunities offered by non-Gaussian quantum states., Comment: 6 Pages, 8 figures

The recent launch of the Micius quantum-enabled satellite heralds a major step forward for long-range quantum communication. Using single-photon discrete-variable quantum states, this exciting new development proves beyond any doubt that all of the quantum protocols previously deployed over limited ranges in terrestrial experiments can, in fact, be translated to global distances via the use of low-orbit satellites. In this work, we survey the imminent extension of space-based quantum communication to the continuous-variable regime - the quantum regime perhaps most closely related to classical wireless communications. The CV regime offers the potential for increased communication performance and represents the next major step forward for quantum communications and the development of the global quantum internet., Comment: Submitted to IEEE Communications Surveys and Tutorials. Contains updated references

In this work we explore the security of secret keys generated via the electromagnetic reciprocity of the wireless fading channel. Identifying a new sophisticated colluding attack, we explore the information-theoretic-security for such keys in the presence of an all-powerful adversary constrained only by the laws of quantum mechanics. Specifically, we calculate the reduction in the conditional mutual information between transmitter and receiver that can occur when an adversary with unlimited computational and communication resources places directional antenna interceptors at chosen locations. Such locations, in principal, can be arbitrarily far from the intended receiver yet still influence the secret key rate., Comment: 4 pages, 2 figures. This work has been submitted to the IEEE for possible publication

In this work we analyse the structure of highly-entangled multimode squeezed states, such as those generated by broadband pulses undergoing type-II parametric down-conversion (PDC). Such down-conversion has previously been touted as a natural and efficient means of cluster-state generation, and therefore a viable future pathway to quantum computation. We first detail how broadband PDC processes lead directly to a series of orthogonal supermodes that are linear combinations of the original frequency modes. We then calculate the total squeezing of the multimode entangled states when they are assumed to be measured by an ideal homodyne detection in which all supermodes of the states are detected by an optimally shaped local oscillator (LO) pulse. For comparison, squeezing of the same entangled states are calculated when measured by a lower-complexity homodyne detection scheme that exploits an unshaped LO pulse. Such calculations illustrate the cost, in the context of squeezing, of moving from higher complexity (harder to implement) homodyne detection to lower-complexity (easier-to-implement) homodyne detection. Finally, by studying the degradation in squeezing of the supermodes under photonic loss, multimode entangled state evolution through an attenuation channel is determined. The results reported here push us towards a fuller understanding of the real-world transfer of cluster-states when they take the form of highly-entangled multimode states in frequency space., Comment: Accepted for publication: IEEE VTC International Workshop on Quantum Communications for Future Networks (QCFN), Sydney, Australia, June 2017