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Quantum key distribution can provide information-theoretical secure communication, which is now heading towards building the quantum secure network for real-world applications. In most built quantum secure networks, point-to-multipoint (PTMP) topology is one of the most popular schemes, especially for quantum access networks. However, due to the lack of custom protocols with high secret key rate and compatible with classical optical networks for PTMP scheme, there is still no efficient way for a high-performance quantum access network with a multitude of users. Here, we report an experimental demonstration of a high-rate 16-nodes quantum access network based on passive optical network, where a high-efficient coherent-state PTMP protocol is novelly designed to allow independent secret key generation between one transmitter and multiple receivers concurrently. Such accomplishment is attributed to a well-designed real-time shot-noise calibration method, a series of advanced digital signal processing algorithms and a flexible post-processing strategy with high success probability. Finally, the experimental results show that the average secret key rate is around 2.086 Mbps between the transmitter and each user, which is two orders of magnitude higher than previous demonstrations. With the advantages of low cost, excellent compatibility, and wide bandwidth, our work paves the way for building practical PTMP quantum access networks, thus constituting an important step towards scalable quantum secure networks.

Quantum illumination (QI) and quantum radar have emerged as potentially groundbreaking technologies, leveraging the principles of quantum mechanics to revolutionise the field of remote sensing and target detection. The protocol, particularly in the context of quantum radar, has been subject to a great deal of aspirational conjecture as well as criticism with respect to its realistic potential. In this review, we present a broad overview of the field of quantum target detection focusing on QI and its potential as an underlying scheme for a quantum radar operating at microwave frequencies. We provide context for the field by considering its historical development and fundamental principles. Our aim is to provide a balanced discussion on the state of theoretical and experimental progress towards realising a working QI-based quantum radar, and draw conclusions about its current outlook and future directions.

We discuss the limitations imposed on entanglement distribution, quantum teleportation, and quantum communication by holographic bounds, such as the Bekenstein bound and Susskind's spherical entropy bound. For continuous-variable (CV) quantum information, we show how the naive application of holographic corrections disrupts well-established results. These corrections render perfect CV teleportation impossible, preclude uniform convergence in the teleportation simulation of lossy quantum channels, and impose a revised PLOB bound for quantum communication. While these mathematical corrections do not immediately impact practical quantum technologies, they are critical for a deeper theoretical understanding of quantum information theory.

When analysing Quantum Key Distribution (QKD) protocols several metrics can be determined, but one of the most important is the Secret Key Rate. The Secret Key Rate is the number of bits per transmission that result in being part of a Secret Key between two parties. There are equations that give the Secret Key Rate, for example, for the BB84 protocol, equation 52 from [1, p.1032] gives the Secret Key Rate for a given Quantum Bit Error Rate (QBER). However, the analysis leading to equations such as these often rely on an Asymptotic approach, where it is assumed that an infinite number of transmissions are sent between the two communicating parties (henceforth denoted as Alice and Bob). In a practical implementation this is obviously impossible. Moreover, some QKD protocols belong to a category called Asymmetric protocols, for which it is significantly more difficult to perform such an analysis. As such, there is currently a lot of investigation into a different approach called the Finite-key regime. Work by Bunandar et al. [2] has produced code that used Semi-Definite Programming to produce lower bounds on the Secret Key Rate of even Asymmetric protocols. Our work looks at devising a novel QKD protocol taking inspiration from both the 3-state version of BB84 [3], and the Twin-Field protocol [4], and then using this code to perform analysis of the new protocol., Comment: This manuscript was uploaded to the arXiv by the first author, without approval from co-authors. It is working in progress and contains issues that need to be addressed

The challenge of pattern recognition is to invoke a strategy that can accurately extract features of a dataset and classify its samples. In realistic scenarios this dataset may be a physical system from which we want to retrieve information, such as in the readout of optical classical memories. The theoretical and experimental development of quantum reading has demonstrated that the readout of optical memories can be dramatically enhanced through the use of quantum resources (namely entangled input-states) over that of the best classical strategies. However, the practicality of this quantum advantage hinges upon the scalability of quantum reading, and up to now its experimental demonstration has been limited to individual cells. In this work, we demonstrate for the first time quantum advantage in the multi-cell problem of pattern recognition. Through experimental realizations of digits from the MNIST handwritten digit dataset, and the application of advanced classical post-processing, we report the use of entangled probe states and photon-counting to achieve quantum advantage in classification error over that achieved with classical resources, confirming that the advantage gained through quantum sensors can be sustained throughout pattern recognition and complex post-processing. This motivates future developments of quantum-enhanced pattern recognition of bosonic-loss within complex domains.

Advances in satellite quantum communications aim at reshaping the global telecommunication network by increasing the security of the transferred information. Here, we study the effects of atmospheric turbulence in continuous-variable entanglement distribution and quantum teleportation in the optical regime between a ground station and a satellite. More specifically, we study the degradation of entanglement due to various error sources in the distribution, namely, diffraction, atmospheric attenuation, turbulence, and detector inefficiency, in both downlink and uplink scenarios. As the fidelity of a quantum teleportation protocol using these distributed entangled resources is not sufficient, we include an intermediate station for either state generation, or beam refocusing, in order to reduce the effects of atmospheric turbulence and diffraction, respectively. The results show the feasibility of free-space entanglement distribution and quantum teleportation in downlink paths up to the LEO region, but also in uplink paths with the help of the intermediate station. Finally, we complete the study with microwave-optical comparison in bad weather situations, and with the study of horizontal paths in ground-to-ground and inter-satellite quantum communication.

Port-based teleportation is generalization of the standard teleportation protocol which does not require unitary operations by the receiver. This comes at the price of requiring $N>1$ entangled pairs, while $N=1$ for the standard teleportation protocol. The lack of correction unitaries allows port-based teleportation to be used as a fundamental theoretical tool to simulate arbitrary channels with a general resource, with applications to study fundamental limits of quantum communication, cryptography and sensing, and to define general programmable quantum computers. Here we introduce a general formulation of port-based teleportation in continuous variable systems and study in detail the $N=2$ case. In particular, we interpret the resulting channel as an energy truncation and analyse the kinds of channels that can be naturally simulated after this restriction., Comment: 27 pages, 6 figures. Similar to published version. Supplemental material available in the source folder

Modern security proofs of quantum key distribution (QKD) must take finite-size effects and composable aspects into consideration. This is also the case for continuous-variable (CV) protocols which are based on the transmission and detection of bosonic coherent states. In this paper, we refine and advance the previous theory in this area providing a more rigorous formulation for the composable key rate of a generic CV-QKD protocol. Thanks to these theoretical refinements, our general formulas allow us to prove more optimistic key rates with respect to previous literature., Comment: Results largely extended. Improves theory from arXiv:2203.00706, arXiv:2010.04168, and arXiv:1912.11418

With the exponentially increased demands for large bandwidth, it is important to think about the best network platform as well as the security and privacy of the information in communication networks. Millimetre (mm)-waves and terahertz (THz) with high carrier frequency are proposed as the enabling technologies to overcome Shannons channel capacity limit of existing communication systems by providing ultrawide bandwidth signals. Mm-waves and THz are also able to build wireless links compatible with optical communication systems. However, most solid-state components that can operate reasonably efficiently at these frequency ranges (100GHz-10THz), especially sources and detectors, require cryogenic cooling, as is a requirement for most quantum systems. Here, we show that secure mm-waves and THz QKD can be achieved when the sources and detectors operate at cryogenic temperatures down to T= 4K. We compare single-input single-output (SISO) and multiple-input multiple-output (MIMO) Continuous Variable THz Quantum Key Distribution (CVQKD) schemes and find the positive secret key rate in the frequency ranges between f=100 GHz and 1 THz. Moreover, we find that the maximum transmission distance could be extended, the secret key rate could be improved in lower temperatures, and achieve a maximum secrete communication distance of more than 5 km at f=100GHz and T=4K by using 1024*1024 antennas. Our results may contribute to the efforts to develop next-generation secure wireless communication systems and quantum internet for applications from inter-satellite and deep space, to indoor and short-distance communications.

The field of space communications is the realm of communication technologies where diffraction and atmospheric effects, both of which contribute to loss and noise, become overriding. The pertinent questions here are how and at which rate information (secret keys) can be securely transferred (shared) among users under such supposedly severe circumstances. In the present work we study continuous-variable (CV) quantum key distribution (QKD) in a measurement-device-independent (MDI) configuration over free-space optical (FSO) links. We assess the turbulence regime and provide a composable finite-size key rate analysis of the protocol for FSO links. We study both short-range, horizontal communication links as well as slant paths to, e.g., high-altitude platform station (HAPS) systems., Comment: 9 pages, 6 figures

Simulating quantum channels is a fundamental primitive in quantum computing, since quantum channels define general (trace-preserving) quantum operations. An arbitrary quantum channel cannot be exactly simulated using a finite-dimensional programmable quantum processor, making it important to develop optimal approximate simulation techniques. In this paper, we study the challenging setting in which the channel to be simulated varies adversarially with time. We propose the use of matrix exponentiated gradient descent (MEGD), an online convex optimization method, and analytically show that it achieves a sublinear regret in time. Through experiments, we validate the main results for time-varying dephasing channels using a programmable generalized teleportation processor., Comment: submitted for conference publication

The security of prepare-and-measure satellite-based quantum key distribution (QKD), under restricted eavesdropping scenarios, is addressed. We particularly consider cases where the eavesdropper, Eve, has limited access to the transmitted signal by Alice, and/or Bob's receiver station. This restriction is modeled by lossy channels between Alice/Bob and Eve, where the transmissivity of such channels can, in principle, be bounded by monitoring techniques. An artefact of such lossy channels is the possibility of having {\it bypass} channels, those which are not accessible to Eve, but may not necessarily be characterized by the users either. This creates interesting, unexplored, scenarios for analyzing QKD security. In this paper, we obtain generic bounds on the key rate in the presence of bypass channels and apply them to continuous-variable QKD protocols with Gaussian encoding with direct and reverse reconciliation. We find regimes of operation in which the above restrictions on Eve can considerably improve system performance. We also develop customised bounds for several protocols in the BB84 family and show that, in certain regimes, even the simple protocol of BB84 with weak coherent pulses is able to offer positive key rates at high channel losses, which would otherwise be impossible under an unrestricted Eve. In this case the limitation on Eve would allow Alice to send signals with larger intensities than the optimal value under an ideal Eve, which effectively reduces the effective channel loss. In all these cases, the part of the transmitted signal that does not reach Eve can play a non-trivial role in specifying the achievable key rate. Our work opens up new security frameworks for spaceborne quantum communications systems., Comment: 26 pages, 17 figures

Identifying clusters in data is an important task in many fields. In this paper, we consider situations in which data live in a physical world, so we have to first collect the images using sensors before clustering them. Using sensors enhanced by quantum entanglement, we can image surfaces more accurately than using purely classical strategies. However, it is not immediately obvious if the advantage we gain is robust enough to survive data processing steps such as clustering. It has previously been found that using quantum-enhanced sensors for imaging and pattern recognition can give an advantage for supervised learning tasks, and here we demonstrate that this advantage also holds for an unsupervised learning task, namely clustering., Comment: 14 pages, 9 figures. Similar to published version. Supplemental material available at https://github.com/softquanta/clustering

Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding the set of achievable errors, using the trace norm, the fidelity, and the quantum Chernoff bound. The upper bound is asymptotically tight and the lower bound is exact for pure states. Unlike asymptotic bounds, our bounds give error values instead of exponents, so can give more precise results when applied to finite-copy state discrimination problems., Comment: 17 pages, 4 figures. Similar to published version. Supplemental material available in the source folder

Future quantum networks will be hybrid structures, constructed from complex architectures of quantum repeaters interconnected by quantum channels that describe a variety of physical domains; predominantly optical-fiber and free-space links. In this hybrid setting, the interplay between the channel quality within network sub-structures must be carefully considered, and is pivotal for ensuring high-rate end-to-end quantum communication. In this work, we combine recent advances in the theory of point-to-point free-space channel capacities and end-to-end quantum network capacities in order to develop critical tools for the study of hybrid, free-space quantum networks. We present a general formalism for studying the capacities of arbitrary, hybrid quantum networks, before specifying to the regime of atmospheric and space-based quantum channels. We then introduce a class of modular quantum network architectures which offer a realistic and readily analysable framework for hybrid quantum networks. By considering a physically motivated, highly connected modular structure we are able to idealize network performance and derive channel conditions for which optimal performance is guaranteed. This allows us to reveal vital properties for which distance-independent rates are achieved, so that the end-to-end capacity has no dependence on the physical separation between users. Our analytical method elucidates key infrastructure demands for a future satellite-based global quantum internet, and for hybrid wired/wireless metropolitan quantum networks., Comment: Submitted to PRApplied 13/9/21. Published 7/7/22. REVTeX, 35 pages, 8 figures

The optimal performance of a communication network is limited not only by the quality of point-to-point channels, but by the efficacy of its constituent technologies. Understanding the limits of quantum networks requires an understanding of both the ultimate capacities of quantum channels and the efficiency of imperfect quantum repeaters. In this work, using a recently developed node-splitting technique which introduces internal losses and noise into repeater devices, we present achievable end-to-end rates for noisy-repeater quantum networks. These are obtained by extending the coherent and reverse coherent information (single channel capacity lower bounds) into end-to-end capacity lower bounds, both in the context of single-path and multi-path routing. These achievable rates are completely general, and apply to networks composed of arbitrary channels arranged in general topologies. Through this general formalism, we show how tight upper-bounds can also be derived by supplementing appropriate single-edge capacity bounds. As a result, we develop tools which provide tight performance bounds for quantum networks constituent of channels whose capacities are not exactly known, and reveal critical network properties which are necessary for high-rate quantum communications. This permits the investigation of pertinent classes of quantum networks with realistic technologies; qubit amplitude damping networks and bosonic thermal-loss networks., Comment: Submitted to QST on 1/4/22, Published 12/7/22. REVTeX, 19 pages, 3 figures

The performance of a practical continuous-variable (CV) quantum key distribution (QKD) protocol depends significantly, apart from the loss and noise of the quantum channel, on the post-processing steps which lead to the extraction of the final secret key. A critical step is the reconciliation process, especially when one assumes finite-size effects in a composable framework. Here, we focus on the Gaussian-modulated coherent-state protocol with heterodyne detection in a high signal-to-noise ratio regime. We simulate the quantum communication process and we post-process the output data by applying parameter estimation, error correction (using high-rate, non-binary low-density parity-check codes), and privacy amplification. This allows us to study the performance for practical implementations of the protocol and optimize the parameters connected to the steps above. We also present an associated Python library performing the steps above., Comment: 13 pages, 5 figures, 2 tables

A continuous variable (CV), measurement device independent (MDI) quantum key distribution (QKD) protocol is analyzed, enabling three parties to connect for quantum conferencing. We utilise a generalised Bell detection at an untrusted relay and a postselection procedure, in which distant parties reconcile on the signs of the displacements of the quadratures of their prepared coherent states. We derive the rate of the protocol under a collective pure-loss attack, demonstrating improved rate-distance performance compared to the equivalent non-post-selected protocol. In the symmetric configuration in which all the parties lie the same distance from the relay, we find a positive key rate over 6 km. Such postselection techniques can be used to improve the rate of multi-party quantum conferencing protocols at longer distances at the cost of reduced performance at shorter distances., Comment: 9 pages, 3 figures

Gaussian networks are fundamental objects in network information theory. Here many senders and receivers are connected by physically motivated Gaussian channels while auxiliary Gaussian components, such as Gaussian relays, are entailed. Whilst the theoretical backbone of classical Gaussian networks is well established, the quantum analogue is yet immature. Here, we theoretically tackle composable security of arbitrary Gaussian quantum networks (quantum networks), with generally untrusted nodes, in the finite-size regime. We put forward a general methodology for parameter estimation, which is only based on the data shared by the remote end-users. Taking a chain of identical quantum links as an example, we further demonstrate our study. Additionally, we find that the key rate of a quantum amplifier-assisted chain can ideally beat the fundamental repeaterless limit with practical block sizes. However, this objective is practically questioned leading the way to new network/chain designs., Comment: 12 pages, 5 figures

Continuous variable (CV) quantum key distribution (QKD) provides a powerful setting for secure quantum communications, thanks to the use of room-temperature off-the-shelf optical devices and the potential to reach much higher rates than the standard discrete-variable counterpart. In this work, we provide a general framework for studying the composable finite-size security of CV-QKD with Gaussian-modulated coherent-state protocols under various levels of trust for the loss and noise experienced by the parties. Our study considers both wired (i.e., fiber-based) and wireless (i.e., free-space) quantum communications. In the latter case, we show that high key rates are achievable for short-range optical wireless (LiFi) in secure quantum networks with both fixed and mobile devices. Finally, we extend our investigation to microwave wireless (WiFi) discussing security and feasibility of CV-QKD for very short-range applications., Comment: Submitted to PRR on 11/07/2021. Accepted on 21/9/2021. Published on 7/10/2021. REVTeX. 18 pages, 7 figures

Quantum target detection aims to utilise quantum technologies to achieve performances in target detection not possible through purely classical means. Quantum illumination is an example of this, based on signal-idler entanglement, promising a potential 6 dB advantage in error exponent over its optimal classical counterpart. So far, receiver designs achieving this optimal reception remain elusive with many proposals based on Gaussian processes appearing unable to utilise quantum information contained within Gaussian state sources. This paper considers the employment of a noiseless linear amplifier at the detection stage of a quantum illumination-based quantum target detection protocol. Such a non-Gaussian amplifier offers a means of probabilistically amplifying an incoming signal without the addition of noise. Considering symmetric hypothesis testing, the quantum Chernoff bound is derived and limits on detection error probability is analysed for both the two-mode squeezed vacuum state and the coherent state classical benchmark. Our findings show that in such a scheme the potential quantum advantage is amplified even in regimes where quantum illumination alone offers no advantage, thereby extending its potential use. The same cannot be said for coherent states, whose performances are generally bounded by that without amplification., Comment: In press at Quantum Science and Technology

The derivation of ultimate limits to communication over certain quantum repeater networks have provided extremely valuable benchmarks for assessing near-term quantum communication protocols. However, these bounds are usually derived in the limit of ideal devices and leave questions about the performance of practical implementations unanswered. To address this challenge, we quantify how the presence of loss in repeater stations affect the maximum attainable rates for quantum communication over linear repeater chains and more complex quantum networks. Extending the framework of node splitting, we model the loss introduced at the repeater stations and then prove the corresponding limits. In the linear chain scenario we show that, by increasing the number of repeater stations, the maximum rate cannot overcome a quantity which solely depends on the loss of a single station. We introduce a way of adapting the standard machinery for obtaining bounds to this realistic scenario. The difference is that whilst ultimate limits for any strategy can be derived given a fixed channel, when the repeaters introduce additional decoherence, then the effective overall channel is itself a function of the chosen repeater strategy (e.g., one-way versus two-way classical communication). Classes of repeater strategies can be analysed using additional modelling and the subsequent bounds can be interpreted as the optimal rate within that class., Comment: 13 pages, 5 figures, replaced with final version

A quantum key distribution (QKD) system must fulfill the requirement of universal composability to ensure that any cryptographic application (using the QKD system) is also secure. Furthermore, the theoretical proof responsible for security analysis and key generation should cater to the number $N$ of the distributed quantum states being finite in practice. Continuous-variable (CV) QKD based on coherent states, despite being a suitable candidate for integration in the telecom infrastructure, has so far been unable to demonstrate composability as existing proofs require a rather large $N$ for successful key generation. Here we report the first Gaussian-modulated coherent state CVQKD system that is able to overcome these challenges and can generate composable keys secure against collective attacks with $N \lesssim 3.5\times10^8$ coherent states. With this advance, possible due to novel improvements to the security proof and a fast, yet low-noise and highly stable system operation, CVQKD implementations take a significant step towards their discrete-variable counterparts in practicality, performance, and security., Comment: 8 pages (including 3 figures and references) + 12 pages supplement

Due to the difficulties of implementing joint measurements, quantum illumination schemes that are based on signal-idler entanglement are difficult to implement in practice. For this reason, one may consider quantum-inspired designs of quantum lidar/radar where the input sources are semiclassical (coherent states) while retaining the quantum aspects of the detection. The performance of these designs could be studied in the context of asymmetric hypothesis testing by resorting to the quantum Stein's lemma. However, here we discuss that, for typical finite-size regimes, the second- and third-order expansions associated with this approach are not sufficient to prove quantum advantage.

Channel position finding is the task of determining the location of a single target channel amongst an ensemble of background channels. It has many potential applications, including quantum sensing, quantum reading and quantum spectroscopy. In particular, it could allow for simple detection protocols to be extended to ones of measurement, for example, target ranging with quantum illumination. The use of quantum states and entanglement in such protocols have shown to yield quantum advantages over their optimal classical counterparts. Here we consider quantum channel position finding using sources specified by at most one single photon on average per mode, using the discrete variable formalism. By considering various quantum sources it is shown through the derivation of performance bounds that a quantum enhancement may be realised.

It is not clear if the performance of a quantum lidar or radar, without an idler and only using Gaussian resources, could exceed the performance of a semiclassical setup based on coherent states and homodyne detection. Here we prove this is indeed the case by showing that an idler-free squeezed-based setup can beat this semiclassical benchmark. More generally, we show that probes whose displacement and squeezing are jointly optimized can strictly outperform coherent states with the same mean number of input photons for both the problems of quantum illumination and reading., Comment: Second revision. Accepted in Physical Review Research

An important theorem in Gaussian quantum information tells us that we can diagonalise the covariance matrix of any Gaussian state via a symplectic transformation. Whilst the diagonal form is easy to find, the process for finding the diagonalising symplectic can be more difficult, and a common, existing method requires taking matrix powers, which can be demanding analytically. Inspired by a recently presented technique for finding the eigenvectors of a Hermitian matrix from certain submatrix eigenvalues, we derive a similar method for finding the diagonalising symplectic from certain submatrix determinants, which could prove useful in Gaussian quantum information., Comment: 10 pages, supplementary files available at https://github.com/softquanta/symplectic_decomposition

Since the invention of the laser in the 60s, one of the most fundamental communication channels has been the free-space optical channel. For this type of channel, a number of effects generally need to be considered, including diffraction, refraction, atmospheric extinction, pointing errors and, most importantly, turbulence. Because of all these adverse features, the free-space optical (FSO) channel is more difficult to study than a stable fiber-based link. For the same reasons, only recently it has been possible to establish the ultimate performances achievable in quantum communications via free-space channels, together with practical rates for continuous variable (CV) quantum key distribution (QKD). Differently from previous literature, mainly focused on the regime of weak turbulence, this work considers the FSO channel in the more challenging regime of moderate-to-strong turbulence, where effects of beam widening and breaking are more important than beam wandering. This regime may occur in long-distance free-space links on the ground, in uplink to high-altitude platform systems (HAPS) and, more interestingly, in downlink from near-horizon satellites. In such a regime we rigorously investigate ultimate limits for quantum communications and show that composable keys can be extracted using CV-QKD., Comment: 13 pages

We investigate the performance of Gaussianmodulated coherent-state QKD protocols in the presence of canonical attacks, which are collective Gaussian attacks resulting in Gaussian channels described by one of the possible canonical forms. We present asymptotic key rates and then we extend the results to the finite-size regime using a recently-developed toolbox for composable security., Comment: 6 pages, 4 figures

Quantum illumination (QI) theoretically promises up to a 6dB error-exponent advantage in target detection over the best classical protocol. The advantage is maximised by a regime which includes a very high background, which occurs naturally when one considers microwave operation. Such a regime has well-known practical limitations, though it is clear that, theoretically, knowledge of the associated classical benchmark in the microwave is lacking. The requirement of amplifiers for signal detection necessarily renders the optimal classical protocol here different to that which is traditionally used, and only applicable in the optical domain. In this work we outline what is the true classical benchmark for microwave QI using coherent states, providing new bounds on the error probability and closed formulae for the receiver operating characteristic (ROC), for both optimal (based on quantum relative entropy) and homodyne detection schemes. We also propose an alternative source generation procedure based on coherent states which demonstrates potential to reach classically optimal performances achievable in optical applications. We provide the same bounds and measures for the performance of such a source and discuss its potential utility in the future of room temperature quantum detection schemes in the microwave.

Protocols for discriminating between a pair of channels or for estimating a channel parameter can often be aided by adaptivity or by entanglement between the probe states. This can make it difficult to bound the best possible performance for such protocols. In this paper, we introduce a quantity that we call the relative fidelity of a given pair of channels and a pair of input states to those channels. Constraining the allowed input states to all pairs of states whose fidelity is greater than some minimum "input fidelity" and minimising this quantity over the valid pairs of states, we get the minimum relative fidelity for that input fidelity constraint. We are then able to lower bound the fidelity between the possible output states of any protocol acting on one of two possible channels in terms of the minimum relative fidelity. This allows us to bound the performance of the most general, adaptive discrimination and parameter estimation protocols. By finding a continuity bound for the relative fidelity, we also provide a simple confirmation that the quantum Fisher information (QFI) of the output of an $N$-use protocol is no more than $N^2$ times the one-shot QFI., Comment: 13 pages, 3 figures, supplementary files available at https://doi.org/10.5281/zenodo.5498138. Similar to published version

The development of a future, global quantum communication network (or quantum internet) will enable high rate private communication and entanglement distribution over very long distances. However, the large-scale performance of ground-based quantum networks (which employ photons as information carriers through optical-fibres) is fundamentally limited by fibre quality and link length, with the latter being a primary design factor for practical network architectures. While these fundamental limits are well established for arbitrary network topologies, the question of how to best design global architectures remains open. In this work, we introduce a large-scale quantum network model called weakly-regular architectures. Such networks are capable of idealising network connectivity, provide freedom to capture a broad class of spatial topologies and remain analytically treatable. This allows us to investigate the effectiveness of large-scale networks with consistent connective properties, and unveil critical conditions under which end-to-end rates remain optimal. Furthermore, through a strict performance comparison of ideal, ground-based quantum networks with that of realistic satellite quantum communication protocols, we establish conditions for which satellites can be used to outperform fibre-based quantum infrastructure; {rigorously proving the efficacy of satellite-based technologies for global quantum communications., Comment: Revised Version. Main text: 11 pages, 3 figures; Supplementary Mat. 19 pages, 4 figures

Continuous-variable (CV) quantum key distribution (QKD) employs the quadratures of a bosonic mode to establish a secret key between two remote parties, and this is usually achieved via a Gaussian modulation of coherent states. The resulting secret key rate depends not only on the loss and noise in the communication channel, but also on a series of data processing steps that are needed for transforming shared correlations into a final string of secret bits. Here we consider a Gaussian-modulated coherent-state protocol with homodyne detection in the general setting of composable finite-size security. After simulating the process of quantum communication, the output classical data is post-processed via procedures of parameter estimation, error correction, and privacy amplification. In particular, we analyze the high signal-to-noise regime which requires the use of high-rate (non-binary) low-density parity check codes. We implement all these steps in a Python-based library that allows one to investigate and optimize the protocol parameters to be used in practical experimental implementations of short-range CV-QKD., Comment: Accepted version. The code for data-processing is available on github at https://github.com/softquanta/homCVQKD

We propose a multi-mode modulation scheme for Continuous Variable (CV) quantum communications, which we call quantum pattern encoding. In this setting, classical information can be encoded into multi-mode patterns of discretely-modulated coherent states, which form instances of a communicable image space. Communicators can devise arbitrarily complex encoding schemes which are degenerate and highly non-uniform, such that communication is likened to the task of pattern recognition. We explore initial communication schemes that exploit these techniques, and which lead to an increased encoding complexity. We discuss the impact that this has on the role of a near-term quantum eavesdropper; formulating new, realistic classes of attacks and secure communication rates., Comment: Accepted Version. 13 pages, 4 figures

Concerted efforts are underway to establish an infrastructure for a global quantum internet to realise a spectrum of quantum technologies. This will enable more precise sensors, secure communications, and faster data processing. Quantum communications are a front-runner with quantum networks already implemented in several metropolitan areas. A number of recent proposals have modelled the use of space segments to overcome range limitations of purely terrestrial networks. Rapid progress in the design of quantum devices have enabled their deployment in space for in-orbit demonstrations. We review developments in this emerging area of space-based quantum technologies and provide a roadmap of key milestones towards a complete, global quantum networked landscape. Small satellites hold increasing promise to provide a cost effective coverage required to realised the quantum internet. We review the state of art in small satellite missions and collate the most current in-field demonstrations of quantum cryptography. We summarise important challenges in space quantum technologies that must be overcome and recent efforts to mitigate their effects. A perspective on future developments that would improve the performance of space quantum communications is included. We conclude with a discussion on fundamental physics experiments that could take advantage of a global, space-based quantum network., Comment: 26 pages, 9 figures. Comments welcome. This paper is a preprint of a paper submitted to IET Quantum Communication. If accepted, the copy of record will be available at the IET Digital Library

The protocol of quantum reading refers to the quantum enhanced retrieval of information from an optical memory, whose generic cell stores a bit of information in two possible lossy channels. In the following we analyze the case of a particular class of optical receiver, based on photon counting measurement, since they can be particularly simple in view of real applications. We show that a quantum advantage is achievable when a transmitter based on two-mode squeezed vacuum (TMSV) states is combined with a photon counting receiver, and we experimentally confirm it. In this paper, after introducing some theoretical background, we focus on the experimental realisation, describing the data collection and the data analysis in detail.

Quantum classification and hypothesis testing are two tightly related subjects, the main difference being that the former is data driven: how to assign to quantum states $\rho(x)$ the corresponding class $c$ (or hypothesis) is learnt from examples during training, where $x$ can be either tunable experimental parameters or classical data "embedded" into quantum states. Does the model generalize? This is the main question in any data-driven strategy, namely the ability to predict the correct class even of previously unseen states. Here we establish a link between quantum machine learning classification and quantum hypothesis testing (state and channel discrimination) and then show that the accuracy and generalization capability of quantum classifiers depend on the (R\'enyi) mutual informations $I(C{:}Q)$ and $I_2(X{:}Q)$ between the quantum state space $Q$ and the classical parameter space $X$ or class space $C$. Based on the above characterization, we then show how different properties of $Q$ affect classification accuracy and generalization, such as the dimension of the Hilbert space, the amount of noise, and the amount of neglected information from $X$ via, e.g., pooling layers. Moreover, we introduce a quantum version of the Information Bottleneck principle that allows us to explore the various tradeoffs between accuracy and generalization. Finally, in order to check our theoretical predictions, we study the classification of the quantum phases of an Ising spin chain, and we propose the Variational Quantum Information Bottleneck (VQIB) method to optimize quantum embeddings of classical data to favor generalization., Comment: 19 pages, 7 figures. Updated version with better connection to quantum hypothesis testing, new numerical applications for quantum phase recognition and for training quantum embeddings

Reliable methods for the classification and quantification of quantum entanglement are fundamental to understanding its exploitation in quantum technologies. One such method, known as Separable Neural Network Quantum States (SNNS), employs a neural network inspired parameterisation of quantum states whose entanglement properties are explicitly programmable. Combined with generative machine learning methods, this ansatz allows for the study of very specific forms of entanglement which can be used to infer/measure entanglement properties of target quantum states. In this work, we extend the use of SNNS to mixed, multipartite states, providing a versatile and efficient tool for the investigation of intricately entangled quantum systems. We illustrate the effectiveness of our method through a number of examples, such as the computation of novel tripartite entanglement measures, and the approximation of ultimate upper bounds for qudit channel capacities., Comment: 14 pages, 7 figures

The global interest in quantum networks stems from the security guaranteed by the laws of physics. Deploying quantum networks means facing the challenges of scaling up the physical hardware and, more importantly, of scaling up all other network layers and optimally utilising network resources. Here we consider two related protocols, their experimental demonstrations on an 8-user quantum network test-bed, and discuss their usefulness with the aid of example use cases. First, an authentication transfer protocol to manage a fundamental limitation of quantum communication -- the need for a pre-shared key between every pair of users linked together on the quantum network. By temporarily trusting some intermediary nodes for a short period of time (<35 min in our network), we can generate and distribute these initial authentication keys with a very high level of security. Second, when end users quantify their trust in intermediary nodes, our flooding protocol can be used to improve both end-to-end communication speeds and increase security against malicious nodes., Comment: New version includes changes suggested by referees, and a modification to an incorrect calculation. Fig. 6 has been updated correspondingly. With thanks to Rui Wang for spotting the mistake, and the referees for detailed feedback

The ability to precisely discriminate multiple quantum channels is fundamental to achieving quantum enhancements in data-readout, target detection, pattern recognition, and more. Optimal discrimination protocols often rely on entanglement shared between an incident probe and a protected idler-mode. While these protocols can be highly advantageous over classical ones, the storage of idler-modes is extremely challenging in practice. In this work, we investigate idler-free block protocols based on the use of multipartite entangled probe states. In particular, we focus on a class of idler-free protocol which uses non-disjoint distributions of multipartite probe states irradiated over multi-channels, known as dynamic discrimination protocols. We derive new, analytical bounds for the average error probability of such protocols in a bosonic Gaussian channel setting, revealing idler-free strategies that display performance close to idler-assistance for powerful, near-term quantum sensing applications., Comment: 22 pages, 5 figures. Close to accepted version

Quantum Hypothesis Testing has shown the advantages that quantum resources can offer in the discrimination of competing hypothesis. Here, we apply this framework to optomechanical systems and fundamental physics questions. In particular, we focus on an optomechanical system composed of two cavities employed to perform quantum channel discrimination. We show that input squeezed optical noise, and feasible measurement schemes on the output cavity modes, allow to obtain an advantage with respect to any comparable classical schemes. We apply these results to the discrimination of models of spontaneous collapse of the wavefunction, highlighting the possibilities offered by this scheme for fundamental physics searches., Comment: 10 pages, 10 figures, 1 table

Satellite quantum communications are emerging within the panorama of quantum technologies as a more effective strategy to distribute completely-secure keys at very long distances, therefore playing an important role in the architecture of a large-scale quantum network. In this work, we apply and extend recent results in free-space quantum communications to determine the ultimate limits at which secret (and entanglement) bits can be distributed via satellites. Our study is comprehensive of the various practical scenarios, encompassing both downlink and uplink configurations, with satellites at different altitudes and zenith angles. It includes effects of diffraction, extinction, background noise and fading, due to pointing errors and atmospheric turbulence (appropriately developed for slant distances). Besides identifying upper bounds, we also discuss lower bounds, i.e., achievable rates for key generation and entanglement distribution. In particular, we study the composable finite-size secret key rates that are achievable by protocols of continuous variable quantum key distribution, for both downlink and uplink, showing the feasibility of this approach for all configurations. Finally, we present a study with a sun-synchronous satellite, showing that its key distribution rate is able to outperform a ground chain of ideal quantum repeaters., Comment: Main results: (1) Ultimate bounds for quantum communications with satellites (QKD/entanglement distribution); (2) Achievable secret-key rates with composable finite-size security, showing the feasibility of high-rate CV-QKD with a satellite in all configurations (downlink/uplink - night/day); (3) Comparison between a sun-synchronous satellite and a ground chain of quantum repeaters

While quantum illumination (QI) can offer a quantum-enhancement in target detection, its potential for performing target ranging remains unclear. With its capabilities hinging on a joint-measurement between a returning signal and its retained idler, an unknown return time makes a QI-based protocol difficult to realise. This paper outlines a potential QI-based approach to quantum target ranging based on recent developments in multiple quantum hypothesis testing and quantum-enhanced channel position finding (CPF). Applying CPF to time bins, one finds an upper-bound on the error probability for quantum target ranging. However, using energetic considerations, we show that for such a scheme a quantum advantage may not physically be realised., Comment: 4 pages, 2 figures

The characterisation of Quantum Channel Discrimination (QCD) offers critical insight for future quantum technologies in quantum metrology, sensing and communications. The task of multi-channel discrimination creates a scenario in which the discrimination of multiple quantum channels can be equated to the idea of pattern recognition, highly relevant to the tasks of quantum reading, illumination and more. Whilst the optimal quantum strategy for many scenarios is an entangled idler-assisted protocol, the extension to a multi-hypothesis setting invites the exploration of discrimination strategies based on unassisted, multipartite probe states. In this work, we expand the space of possible quantum enhanced protocols by formulating general classes of unassisted multi-channel discrimination protocols which are not assisted by idler modes. Developing a general framework for idler-free protocols, we perform an explicit investigation in the bosonic setting, studying prominent Gaussian channel discrimination problems for real world applications. Our findings uncover the existence of strongly quantum advantageous, idler-free protocols for the discrimination of bosonic loss and environmental noise. This circumvents the necessity for idler assistance to achieve quantum advantage in some of the most relevant discrimination settings, significantly loosening practical requirements for prominent quantum sensing applications., Comment: 18 pages, 7 figures. Close to accepted version

Quantum Channel Discrimination (QCD) presents a fundamental task in quantum information theory, with critical applications in quantum reading, illumination, data-readout and more. The extension to multiple quantum channel discrimination has seen a recent focus to characterise potential quantum advantage associated with quantum enhanced discriminatory protocols. In this paper, we study thermal imaging as an environment localisation task, in which thermal images are modelled as ensembles of Gaussian phase insensitive channels with identical transmissivity, and pixels possess properties according to background (cold) or target (warm) thermal channels. Via the teleportation stretching of adaptive quantum protocols, we derive ultimate limits on the precision of pattern classification of abstract, binary thermal image spaces, and show that quantum enhanced strategies may be used to provide significant quantum advantage over known optimal classical strategies. The environmental conditions and necessary resources for which advantage may be obtained are studied and discussed. We then numerically investigate the use of quantum enhanced statistical classifiers, in which quantum sensors are used in conjunction with machine learning image classification methods. Proving definitive advantage in the low loss regime, this work motivates the use of quantum enhanced sources for short-range thermal imaging and detection techniques for future quantum technologies., Comment: 15 pages, 7 figures. Close to published version

Entanglement is a powerful tool for quantum sensing, and entangled states can greatly boost the discriminative power of protocols for quantum illumination, quantum metrology, or quantum reading. However, entangled state protocols generally require the retention of an idler state, to which the probes are entangled. Storing a quantum state is difficult and so technological limitations can make protocols requiring quantum memories impracticable. One alternative is idler-free protocols that utilise non-classical sources but do not require any idler states to be stored. Here we apply such a protocol to the task of channel position finding. This involves finding a target channel in a sequence of background channels, and has many applications, including quantum sensing, quantum spectroscopy, and quantum reading., Comment: 13 pages, 8 figures. Similar to published version

The study of free-space quantum communications requires tools from quantum information theory, optics and turbulence theory. Here we combine these tools to bound the ultimate rates for key and entanglement distribution through a free-space link, where the propagation of quantum systems is generally affected by diffraction, atmospheric extinction, turbulence, pointing errors, and background noise. Besides establishing ultimate limits, we also show that the composable secret-key rate achievable by a suitable (pilot-guided and post-selected) coherent-state protocol is sufficiently close to these limits, therefore showing the suitability of free-space channels for high-rate quantum key distribution. Our work provides analytical tools for assessing the composable finite-size security of coherent-state protocols in general conditions, from the standard assumption of a stable communication channel (as is typical in fiber-based connections) to the more challenging scenario of a fading channel (as is typical in free-space links)., Comment: Results of the paper: (i) Ultimate limits/capacities of free-space quantum communications; (ii) General analytical toolbox for composable security analysis of CV-QKD protocols under general conditions (fiber and free-space). REVTeX 36 pages. 6 figures

Quantum hypothesis testing is one of the most fundamental problems in quantum information theory, with crucial implications in areas like quantum sensing, where it has been used to prove quantum advantage in a series of binary photonic protocols, e.g., for target detection or memory cell readout. In this work, we generalize this theoretical model to the multi-partite setting of barcode decoding and pattern recognition. We start by defining a digital image as an array or grid of pixels, each pixel corresponding to an ensemble of quantum channels. Specializing each pixel to a black and white alphabet, we naturally define an optical model of barcode. In this scenario, we show that the use of quantum entangled sources, combined with suitable measurements and data processing, greatly outperforms classical coherent-state strategies for the tasks of barcode data decoding and classification of black and white patterns. Moreover, introducing relevant bounds, we show that the problem of pattern recognition is significantly simpler than barcode decoding, as long as the minimum Hamming distance between images from different classes is large enough. Finally, we theoretically demonstrate the advantage of using quantum sensors for pattern recognition with the nearest neighbor classifier, a supervised learning algorithm, and numerically verify this prediction for handwritten digit classification., Comment: 17 pages, 4 figures

Spectroscopy is an important tool for probing the properties of materials, chemicals and biological samples. We design a practical transmitter-receiver system that exploits entanglement to achieve a provable quantum advantage over all spectroscopic schemes based on classical sources. To probe the absorption spectra, modelled as pattern of transmissivities among different frequency modes, we employ broad-band signal-idler pairs in two-mode squeezed vacuum states. At the receiver side, we apply photodetection after optical parametric amplification. Finally, we perform a maximal-likehihood decision test on the measurement results, achieving orders-of-magnitude-lower error probability than the optimum classical systems in various examples, including `wine-tasting' and `drug-testing' where real molecules are considered. In detecting the presence of an absorption line, our quantum scheme achieves the optimum performance allowed by quantum mechanics. The quantum advantage in our system is robust against noise and loss, which makes near-term experimental demonstration possible., Comment: 6+16 pages, 6+13 figures, accepted by Phys. Rev. Lett