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Quantum key distribution is emerging as a cutting-edge application of quantum technology, gradually integrating into the industrial landscape. Many protocols employing discrete or continuous variables have been developed over time. Whereas the firsts usually excel in covering longer distances, the seconds are typically superior in producing higher secret key rates at short distances. Present efforts aim to create systems that can exploit both these strengths, foreseeing the future challenge regarding the realization of a quantum network consisting of multiple and heterogeneous interconnected nodes. Within such a context, a possible solution is systems able to efficiently toggle between discrete and continuous variable working modes with hybrid quantum state encoders. Therefore, this study presents a new hybrid encoder based on an iPOGNAC modulator, ensuring compatibility with DV and CV QKD systems that can be assembled entirely with commercial-off-the-shelf components. The proposed scheme is the first supporting DV polarization protocols, thus making it an appealing candidate for space nodes of a future quantum network, given that polarization-based protocols are well suited for space links., Comment: 8 pages, 5 figures

Quantum Key Distribution (QKD) promises to revolutionize the field of security in communication, with applications ranging from state secrets to personal data, making it a key player in the ongoing battle against cyber threats. Reference-Frame-Independent (RFI) QKD aims to simplify QKD implementations by allowing to reduce the requirements of alignment on a shared reference frame. This is done by performing two mutually unbiased measurements on the control states. In this work, we present a novel fully passive receiver for time-bin encoded RFI-QKD. Conversion of time-bin to polarization is employed to perform the required quantum measurement in a fully passive manner. Furthermore, to overcome experimental errors, we retrieved a complete description of our measurement apparatus by employing a recently introduced Quantum Detector Self-Characterization technique, without performing tomographic studies on the detection stage. In fact, the security analysis carried out in this work uses experimentally retrieved Positive Operator Valued Measurements, which consider our receiver defects, substituting the ideal expected operators and thus increasing the overall level of secrecy. Lastly, we conducted a proof-of-principle experiment that validated the feasibility of our method and its applicability to QKD applications., Comment: 13 pages, 6 figures, 1 table

Time-to-Digital Converters (TDCs) are a crucial tool in a wide array of fields, in particular for quantum communication, where time taggers performance can severely affect the quality of the entire application. Nowadays, FPGA-based TDCs present a viable alternative to ASIC ones, once the nonlinear behaviour due to the intrinsic nature of the device is properly mitigated. To compensate said nonlinearities, a calibration procedure is required, usually based on an interpolation methods. Here we present the design and the demonstration of a TDC that is FPGA-based and showing a residual jitter of 27 ps, that is scalable for multichannel operation. The application in Quantum Key Distribution (QKD) is discussed with a unique calibration method based on the exploitation of single-photon detection that does not require to stop the data acquisition or to use any interpolation methods, thus increasing accuracy and removing data loss. The calibration was tested in a relevant environment, investigating the device behaviour between 5{\deg}C and 80{\deg}C. Moreover, our design is capable of continuously streaming up to 12 Mevents/s for up to ~1 week without the TDC overflowing.

Integration of Quantum Key Distribution (QKD) in existing telecommunication infrastructure is crucial for the widespread adoption of this quantum technology, which offers the distillation of unconditionally secure keys between users. In this letter, we report a field trial between the Points of Presence (POPs) placed in Treviso and in Venezia - Mestre, Italy, exploiting the QuKy commercial polarization-based QKD platforms developed by ThinkQuantum srl and two different standards of single-mode optical fibers, i.e. G.652 and G.655, as a quantum channel. In this field trial, several configurations were tested, including the co-existence of classical and quantum signals over the same fiber, providing a direct comparison between the performances of the G.652 and G.655 fiber standards for QKD applications., Comment: 6 pages, 5 figures

Time-bin encoding has been widely used for implementing quantum key distribution (QKD) on optical fiber channels due to its robustness with respect to drifts introduced by the optical fiber. However, due to the use of interferometric structures, achieving stable and low intrinsic Quantum Bit Error rate (QBER) in time-bin systems can be challenging. A key device for decoy-state prepare & measure QKD is represented by the state encoder, that must generate low-error and stable states with different values of mean photon number. Here we propose the MacZac (Mach-Zehder-Sagnac), a time-bin encoder with ultra-low intrinsic QBER (<2e-5) and high stability. The device is based on nested Sagnac and Mach-Zehnder interferometers and uses a single phase modulator for both decoy and state preparation, greatly simplifying the optical setup. The encoder does not require any active compensation or feedback system and it can be scaled for the generation of states with arbitrary dimension. We experimentally realized and tested the device performances as a stand alone component and in a complete QKD experiments. Thanks to the capacity to combine extremely low QBER, high stability and experimental simplicity the proposed device can be used as a key building block for future high-performance, low-cost QKD systems., Comment: 12 pages, 14 figures

Intermodal quantum key distribution enables the full interoperability of fiber networks and free-space channels, which are both necessary elements for the development of a global quantum network. We present a field trial of an intermodal quantum key distribution system in a simple 3-node heterogeneous quantum network - comprised of two polarization-based transmitters and a single receiver - in which the active channel is alternately switched between a free-space link of 620 m and a 17km-long deployed fiber in the metropolitan area of Padova. The performance of the free-space channel is evaluated against the atmospheric turbulence strength of the link. The field trial lasted for several hours in daylight conditions, attesting the interoperability between fiber and free-space channels, with a secret key rate of the order of kbps for both the channels. The QKD hardware and software require no different strategies to work over the two channels, even if the intrinsic characteristics of the links are clearly different. The switching system represents a cost-effective solution for a trusted quantum key distribution network, reducing the number of necessary devices in different network topologies., Comment: accepted version

Quantum correlations between measurements of separated observers are crucial for applications like randomness generation and key distribution. Although device-independent security can be certified with minimal assumptions, current protocols have limited performances. Here, we exploit sequential measurements, defined with a precise temporal order, to enhance performances by reusing quantum states. We provide a geometric perspective and a general mathematical framework, analytically proving a Tsirelson-like boundary for sequential quantum correlations, which represents a trade-off in nonlocality shared by sequential users. This boundary is advantageous for secure quantum randomness generation, certifying maximum bits per state with one remote and two sequential parties, even if one sequential user shares no nonlocality. Our simple qubit protocol reaches this boundary, and numerical analysis shows improved robustness under realistic noise. A photonic implementation confirms feasibility and robustness. This study advances understanding of sequential quantum correlations and offers insights for efficient device-independent protocols., Comment: 19 pages, 7 figures, 1 table, v2: published version

This work aims at investigating the optical transmission system needed for such lightweight sail, taking into account the physical constraints of such unprecedented link and focusing on the optimal scheme for the optical signal emission. In particular, the optical signal is distributed to several emitters on the sail. The light diffraction resulting from the pattern of the emitters acting coherently determines the characteristics of the whole beam transmitted by the sail and of the received signal on the Earth. The performance of the digital communication system using pulse position modulation (PPM) can be assessed and channel coding schemes are proposed. We are using the paradigm for which the entire sail communication system is described as a Tree-of-light: the detectors, CPU, memory and laser transmitter are the central unit, representing the trunk of the tree. The branches of the tree are the waveguides, directed to the sail surface. By means of multimode splitters, the signal is further distributed via the petioles to the emitters, the leaves, realized by grating couplers (GCs), on which this work is more focused.

Precise synchronization between transmitter and receiver is crucial for quantum communication protocols, such as Quantum Key Distribution (QKD), to efficiently correlate the transmitted and received signals and increase the signal-to-noise ratio. In this work, we introduce a synchronization technique that exploits a co-propagating classical optical communication link and test its performance in a free-space QKD system. Previously, existing techniques required additional laser beams or relied on the capability of retrieving the synchronization from the quantum signal itself, though this is not applicable in high channel loss scenarios. On the contrary, our method exploits classical and quantum signals locked to the same master clock, allowing the receiver to synchronize both the classical and quantum communication links by performing a clock-data-recovery routine on the classical signal. In this way, by exploiting the same classical communication already required for post-processing and key generation, no additional hardware is required, and the synchronization can be reconstructed from a high-power signal. Our approach is suitable for both satellite and fiber infrastructures, where a classical and quantum channel can be transmitted through the same link., Comment: 6 pages, 5 figures

A wide range of applications require, by hypothesis, to have access to a high-speed, private, and genuine random source. Quantum Random Number Generators (QRNGs) are currently the sole technology capable of producing true randomness. However, the bulkiness of current implementations significantly limits their adoption. In this work, we present a high-performance source-device independent QRNG leveraging a custom made integrated photonic chip. The proposed scheme exploits the properties of a heterodyne receiver to enhance security and integration to promote spatial footprint reduction while simplifying its implementation. This characteristics could represents a significant advancement toward the development of generators better suited to meet the demands of portable and space applications. The system can deliver secure random numbers at a rate greater than 20 Gbps with a reduced spatial and power footprint., Comment: 9 pages, 7 figures

Global Navigation Satellite Systems (GNSSs), such as GPS and Galileo, provide precise time and space coordinates globally and constitute part of the critical infrastructure of modern society. To reliably operate GNSS, a highly accurate and stable system time is required, such as the one provided by several independent clocks hosted in Precise Timing Facilities (PTFs) around the world. Periodically, the relative clock offset between PTFs is measured to have a fallback system to synchronize the GNSS satellite clocks. The security and integrity of the communication between PTFs is of paramount importance: if compromised, it could lead to disruptions to the GNSS service. Therefore, it is a compelling use-case for protection via Quantum Key Distribution (QKD), since this technology provides information-theoretic security. We have performed a field trial demonstration of such use-case by sharing encrypted time synchronization information between two PTFs, one located in Oberpfaffenhofen (Germany) and one in Matera (Italy) - more than 900km apart as the crow flies. To bridge this large distance, a satellite-QKD system is required, plus a "last-mile" terrestrial link to connect the optical ground station (OGS) to the actual location of the PTF. In our demonstration we have deployed two full QKD systems to protect the last-mile connection at both the locations and have shown via simulation that upcoming QKD satellites will be able to distribute keys between Oberpfaffenhofen and Matera exploiting already existing OGSs.

Time-bin (TB) and energy-time (ET) entanglement are crucial resources for long-distance quantum information processing. Recently, major efforts have been made to produce compact high-quality sources of TB/ET entangled photons based on solid-state integrated technologies. However, these attempts failed to close the so-called "post-selection loophole". Here, we present an integrated photonic general Bell-test chip for genuine (i.e., free of the post-selection loophole) TB and ET entanglement certification. We report a violation of a Bell inequality by more than 10 standard deviations using our device based on the "hug" interferometric scheme. The experiment also demonstrates that the hug scheme, previously exploited for ET entanglement, can also be used for genuine TB entanglement., Comment: 12 pages, 10 figures

Optimizing the brightness of a spontaneous parametric down conversion (SPDC) source is an important task for many quantum information applications. We investigate the optimal focusing conditions to maximize the number of photons produced in an SPDC process and coupled with single-mode fibers. We provide a general expression for the two-photon wavefunction, generalizing previous known results, by considering collinear and non-collinear emission. We present analytical expressions for our results in the thin crystal limit and clarify the relation between different focusing conditions already existing in the literature. Differently from what was previously reported, we show that the optimal ratio between the pump waist and the generated photons waist depends on the emission angle: It is $1/\sqrt2$ for collinear degenerate emission and approaches $1/2$ for larger collection angles. The role of spectral filters is also analyzed. We support and enrich our discussion with numerical simulations, performed for type-I SPDC in a $\beta$ barium borate crystal. For this type of emission, we also investigate the role of the transverse walk-off outside the thin crystal regime., Comment: v1: 13 pages, 7 figures; v2, equivalent to the published version: minor changes to the discussion, added Figure 1, addes Section V-D, no changes to the results

We present a source of states for Quantum Key Distribution (QKD) based on a modular design exploiting the iPOGNAC, a stable, low-error, and calibration-free polarization modulation scheme, for both intensity and polarization encoding. This source is immune to the security vulnerabilities of other state sources such as side channels and some quantum hacking attacks. Furthermore, our intensity modulation scheme allows full tunability of the intensity ratio between the decoy and signal states, and mitigates patterning effects. The source was implemented and tested at the near-infrared optical band around 800 nm, of particular interest for satellite-based QKD. Remarkably, the modularity of the source simplifies its development, testing, and qualification, especially for space missions. For these reasons, our work paves the way for the development of the second generation of QKD satellites that can guarantee excellent performances at higher security levels., Comment: 7 pages, 6 figures

The National Aeronautics and Space Administration's Deep Space Quantum Link mission concept enables a unique set of science experiments by establishing robust quantum optical links across extremely long baselines. Potential mission configurations include establishing a quantum link between the Lunar Gateway moon-orbiting space station and nodes on or near the Earth. In this publication, we summarize the principal experimental goals of the Deep Space Quantum Link mission. These include long-range teleportation, tests of gravitational coupling to quantum states, and advanced tests of quantum nonlocality., Comment: 74 pages, 24 figures

Robust implementation of quantum key distribution requires precise state generation and measurements, as well as a transmission that is resistant to channel disturbances. However, the choice of the optimal encoding scheme is not trivial and depends on external factors such as the quantum channel. In fact, stable and low-error encoders are available for polarization encoding, suitable for free-space channels, whereas time-bin encoding represent a good candidate for fiber-optic channels, as birefingence does not perturb this kind of states. Here we present a cross-encoded scheme where high accuracy quantum states are prepared through a self-compensating, calibration-free polarization modulator and transmitted using a polarization-to-time-bin converter. A hybrid receiver performs both time-of-arrival and polarization measurements to decode the quantum states and successfully leaded to a transmission over 50 km fiber spool without disturbances. Temporal synchronization between the two parties is performed with a qubit-based method that does not require additional hardware to share a clock reference. The system was tested in a 12 hour run and demonstrated good and stable performance in terms of key and quantum bit error rates. The flexibility of our approach represents an important step towards the development of hybrid networks with both fiber-optic and free-space links., Comment: 7 pages, 6 figures

Current technological progress is driving Quantum Key Distribution towards a commercial and world widescale expansion. Its capability to deliver unconditionally secure communication will be a fundamental feature in the next generations of telecommunication networks. Nevertheless, demonstrations of QKD implementation in a real operating scenario and their coexistence with the classical telecom infrastructure are of fundamental importance for reliable exploitation. Here we present a Quantum Key Distribution application implemented overa classical fiber-based infrastructure. By exploiting just a single fiber cable for both the quantum and the classical channel and by using a simplified receiver scheme with just one single-photon detector, we demonstrate the feasibility of low-cost and ready-to-use Quantum Key Distribution systems compatible with standard classical infrastructure., Comment: 5 pages, 5 figures

Free-space ground-to-ground links will be an integral part of future quantum communication networks. The implementation of free-space and fiber links in daylight inter-modal configurations are however still hard to achieve, due to the impact of atmospheric turbulence, which strongly decreases the coupling efficiency into the fiber. In this work, we present a comprehensive model of the performance of a free-space ground-to-ground quantum key distribution (QKD) system based on the efficient-BB84 protocol with active decoy states. Our model takes into account the atmospheric channel contribution, the transmitter and receiver telescope design constraints, the parameters of the quantum source and detectors, and the finite-key analysis to produce a set of requirements and optimal design choices for a QKD system operating under specific channel conditions. The channel attenuation is calculated considering all effects deriving from the atmospheric propagation (absorption, beam broadening, beam wandering, scintillation, and wavefront distortions), as well as the effect of fiber-coupling in the presence of a partial adaptive correction with finite control bandwidth. We find that the channel fluctuation statistics must be considered to correctly estimate the effect of the saturation rate of the single-photon detectors, which may otherwise lead to an overestimation of the secret key rate. We further present strategies to minimize the impact of diffuse atmospheric background in daylight operation by means of spectral and temporal filtering., Comment: improved version

The decoy-state method is a standard enhancement to quantum key distribution (QKD) protocols that has enabled countless QKD experiments with inexpensive light sources. However, new technological advancements might require further theoretical study of this technique. In particular, the decoy-state method is typically described under the assumption of a Poisson statistical distribution for the number of photons in each QKD pulse. This is a practical choice, because prepare-and-measure QKD is often implemented with attenuated lasers, which produce exactly this distribution. However, sources that do not meet this assumption are not guaranteed to be compatible with decoy states. In this work, we provide security bounds for decoy-state QKD using a source with an arbitrary photon emission statistic. We consider both the asymptotic limit of infinite key and the finite-size scenario, and evaluate two common decoy-state schemes: the vacuum+weak and one-decoy protocols. We numerically evaluate the performance of the bounds, comparing three realistic statistical distributions (Poisson, thermal, binomial), showing that they are all viable options for QKD., Comment: 7 pages, 6 figures

This work presents a hardware and software architecture which can be used in those systems that implement practical Quantum Key Distribution (QKD) and Quantum Random Number Generation (QRNG) schemes. This architecture fully exploits the capability of a System-on-a-Chip (SoC) which comprehends both a Field Programmable Gate Array (FPGA) and a dual core CPU unit. By assigning the time-related tasks to the FPGA and the management to the CPU, we built a flexible system with optimized resource sharing on a commercial off-the-shelf (COTS) evaluation board which includes a SoC. Furthermore, by changing the dataflow direction, the versatile system architecture can be exploited as a QKD transmitter, QKD receiver and QRNG control-acquiring unit. Finally, we exploited the dual core functionality and realized a concurrent stream device to implement a practical QKD transmitter where one core continuously receives fresh data at a sustained rate from an external QRNG source while the other operates with the FPGA to drive the qubits transmission to the QKD receiver. The system was successfully tested on a long-term run proving its stability and security. This demonstration paves the way towards a more secure QKD implementation, with fully unconditional security as the QKD states are entirely generated by a true random process and not by deterministic expansion algorithms. Eventually, this enables the realization of a standalone quantum transmitter, including both the random numbers and the qubits generation., Comment: 7 pages, 4 figures

Recently, the European Commission supported by many European countries has announced large investments towards the commercialization of quantum technology (QT) to address and mitigate some of the biggest challenges facing today's digital era - e.g. secure communication and computing power. For more than two decades the QT community has been working on the development of QTs, which promise landmark breakthroughs leading to commercialization in various areas. The ambitious goals of the QT community and expectations of EU authorities cannot be met solely by individual initiatives of single countries, and therefore, require a combined European effort of large and unprecedented dimensions comparable only to the Galileo or Copernicus programs. Strong international competition calls for a coordinated European effort towards the development of QT in and for space, including research and development of technology in the areas of communication and sensing. Here, we aim at summarizing the state of the art in the development of quantum technologies which have an impact in the field of space applications. Our goal is to outline a complete framework for the design, development, implementation, and exploitation of quantum technology in space., Comment: 13 pages, 1 figure

Semi-device independent (Semi-DI) quantum random number generators (QRNG) gained attention for security applications, offering an excellent trade-off between security and generation rate. This paper presents a proof-of-principle time-bin encoding semi-DI QRNG experiments based on a prepare-and-measure scheme. The protocol requires two simple assumptions and a measurable condition: an upper-bound on the prepared pulses' energy. We lower-bound the conditional min-entropy from the energy-bound and the input-output correlation, determining the amount of genuine randomness that can be certified. Moreover, we present a generalized optimization problem for bounding the min-entropy in the case of multiple-input and outcomes in the form of a semidefinite program (SDP). The protocol is tested with a simple experimental setup, capable of realizing two configurations for the ternary time-bin encoding scheme. The experimental setup is easy-to-implement and comprises commercially available off-the-shelf (COTS) components at the telecom wavelength, granting a secure and certifiable entropy source. The combination of ease-of-implementation, scalability, high-security level, and output-entropy make our system a promising candidate for commercial QRNGs., Comment: 9 pages, 8 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

Quantum nonlocality offers a secure way to produce random numbers: their unpredictability is intrinsic and can be certified just by observing the statistic of the measurement outcomes, without assumptions on how they are produced. To do this, entangled pairs are generated and measured to violate a Bell inequality with the outcome statistics. However, after a projective quantum measurement, entanglement is entirely destroyed and cannot be used again. This fact poses an upper bound to the number of random numbers that can be produced from each quantum state when projective measurements are employed. Instead, by using weak measurements, some entanglement can be maintained and reutilized, and a sequence of weak measurements can extract an unbounded amount of randomness from a single state as predicted in Phys. Rev. A 95, 020102(R) (2017). We study the feasibility of these weak measurements, analyze the robustness to imperfections in the quantum state they are applied to, and then test them using an optical setup based on polarization-entangled photon pairs. We show that the weak measurements are realizable, but can improve the performance of randomness generation only in close-to-ideal conditions., Comment: 9 pages, 6 figures

Field-trials are of key importance for novel technologies seeking commercialization and wide-spread adoption. This is certainly also the case for Quantum Key Distribution (QKD), which allows distant parties to distill a secret key with unconditional security. Typically, QKD demonstrations over urban infrastructures require complex stabilization and synchronization systems to maintain a low Quantum Bit Error (QBER) and high secret key rates over time. Here we present a field-trial which exploits a low-complexity self-stabilized hardware and a novel synchronization technique, to perform QKD over optical fibers deployed in the city center of Padua, Italy. In particular, two techniques recently introduced by our research group are evaluated in a real-world environment: the iPOGNAC polarization encoder was used for the preparation of the quantum states, while the temporal synchronization was performed using the Qubit4Sync algorithm. The results here presented demonstrate the validity and robustness of our resource-effective QKD system, that can be easily and rapidly installed in an existing telecommunication infrastructure, thus representing an important step towards mature, efficient and low-cost QKD systems., Comment: 5 pages, 3 figures

Randomness is a central feature of quantum mechanics and an invaluable resource for both classical and quantum technologies. Commonly, in Device-Independent and Semi-Device-Independent scenarios, randomness is certified using projective measurements and the amount of certified randomness is bounded by the dimension of the measured quantum system. In this work, we propose a new Source-Device-Independent protocol, based on Positive Operator Valued Measurement (POVM), which can arbitrarily increase the number of certified bits for any fixed dimension. A tight lower-bound on the quantum conditional min-entropy is derived using only the POVM structure and the experimental expectation values, taking into account the quantum side-information. For symmetrical POVM measurements on the Bloch sphere we have derived closed-form analytical bounds. Finally, we experimentally demonstrate our method with a compact and simple photonic setup that employs polarization-encoded qubits and POVM up to 6 outcomes., Comment: 9 pages, 6 figures

Recently, semi-device independent protocols have attracted increasing attention, guaranteeing security with few hypotheses and experimental simplicity. In this paper, we demonstrate a many-outcomes scheme with the binary phase-shift keying (BPSK) for a semi-device independent protocol based on the energy assumption. We show in theory that the number of certified random bits of the d-outcomes system outperforms the standard scheme (binary-outcomes). Furthermore, we compare the results of two well-known measurement schemes, homodyne and heterodyne detection. Lastly, taking into account the experimental imperfections, we discuss the experimental feasibility of the d-outcome design., Comment: 8 pages, 11 figures

Polarization-encoded free-space Quantum Communication requires a quantum state source featuring fast polarization modulation, long-term stability and a low intrinsic error rate. Here we present a source based on a Sagnac interferometer and composed of polarization maintaining fibers, a fiber polarization beam splitter and an electro-optic phase modulator. The system generates predetermined polarization states with a fixed reference frame in free-space that does not require calibration neither at the transmitter nor at the receiver. In this way we achieve long-term stability and low error rates. A proof-of-concept experiment is also reported, demonstrating a Quantum Bit Error Rate lower than 0.2% for several hours without any active recalibration of the devices., Comment: 6 pages, 2 figures

Randomness is a fundamental feature of quantum mechanics, which is an invaluable resource for both classical and quantum technologies. Practical quantum random number generators (QRNG) usually need to trust their devices, but their security can be jeopardized in case of imperfections or malicious external actions. In this work, we present a robust implementation of a Semi-Device-Independent QRNG that guarantees both security and fast generation rates. The system works in a prepare and measure scenario where measurement and source are untrusted, but a bound on the energy of the prepared states is assumed. Our implementation exploits heterodyne detection, which offers increased generation rate and improved long-term stability compared to alternative measurement strategies. In particular, due to the tomographic properties of heterodyne measurement, we can compensate for fast phase fluctuations via post-processing, avoiding complex active phase stabilization systems. As a result, our scheme combines high security and speed with a simple setup featuring only commercial-off-the-shelf components, making it an attractive solution in many practical scenarios., Comment: 10 pages, 7 figures

Establishing secure communication links at a global scale is a major potential application of quantum information science but also extremely challenging for the underlying technology. While milestone experiments using satellite-to-ground links and exploiting singe-photon encoding for implementing quantum key distribution have shown recently that this goal is achievable, it is still necessary to further investigate practical solutions compatible with classical optical communication systems. Here we examine the feasibility of establishing secret keys in a satellite-to-ground downlink configuration using continuous-variable encoding, which can be implemented using standard telecommunication components certified for space environment and able to operate at high symbol rates. Considering a realistic channel model and state-of-the-art technology, and exploiting an orbit subdivision technique for mitigating fluctuations in the transmission efficiency, we find positive secret key rates for a low-Earth-orbit scenario, while finite-size effects can be a limiting factor for higher orbits. Our analysis determines regions of values for important experimental parameters where secret key exchange is possible and can be used as a guideline for experimental efforts in this direction., Comment: 13 pages, 11 figures

A random access code (RAC) is a strategy to encode a message into a shorter one in a way that any bit of the original can still be recovered with nontrivial probability. Encoding with quantum bits rather than classical ones can improve this probability, but has an important limitation: due to the disturbance caused by standard quantum measurements, qubits cannot be used more than once. However, as recently shown by Mohan, Tavakoli, and Brunner [New J. Phys. 21 083034, (2019)], weak measurements can alleviate this problem, allowing two sequential decoders to perform better than with the best classical RAC. We use single photons to experimentally show that these weak measurements are feasible and nonclassical success probabilities are achievable by two decoders. We prove this for different values of the measurement strength and use our experimental results to put tight bounds on them, certifying the accuracy of our setting. This proves the feasibility of using sequential quantum RACs for quantum information tasks such as the self-testing of untrusted devices., Comment: See also the related work arXiv:2001.04768 of Hammad Anwer et al., appearing on arXiv on the same day of the first submission. V2 includes changes after peer review and copy-editing. 9 pages, 6 figures

We introduce a convenient formalism to evaluate the frequency-shift affecting a light signal propagating on a general curved background. Our formulation, which is based on the laws of geometric optics in a general relativistic setting, allows to obtain a transparent generalization of the Doppler frequency-shift without requiring to perform Local Lorentz transformations. It is easily applicable to stationary spacetimes, and in particular to the near-Earth experiments where geometry is described in the parametrized post-Newtonian approximation. We apply our recipe to evaluate the phase-shift arising in large-scale optical interferometric experiments, as the optical version of the Colella-Overhauser-Werner experiment., Comment: 8 pages, 3 figures

This work presents new techniques to produce true random bits by exploiting single photon time of arrival. Two FPGA-based QRNG devices are presented: Randy which uses one discrete SPAD and LinoSPAD which uses a CMOS SPAD array, along with a time-to-digital converter (TDC). Post-processing procedures are explained in order to extract randomness taking care of SPAD and TDC non-idealities. These procedures are based on the application of Peres [Y. Peres, Ann. Statist.20, 590 (1992)] and Zhou-Bruk [H. Zhou and J. Bruck, arXiv:1209.0726 (2012)] extraction algorithms. Achieved generation rates are 1.8 Mbit/s for Randy device and 310 Mbit/s for LinoSPAD device. Randy QRNG also features a real time procedure which was used for the realization of fundamental tests of physics., Comment: 9 pages, 10 figures

Quantum Key Distribution (QKD) relies on quantum communication to allow distant parties to share a secure cryptographic key. Widespread adoption of QKD in current telecommunication networks will require the development of simple, low cost and stable systems. However, current QKD implementations usually include additional hardware that perform auxiliary tasks such as temporal synchronization and polarization basis tracking. Here we present a polarization-based QKD system operating at 1550 nm that performs synchronization and polarization compensation by exploiting only the hardware already needed for the quantum communication task. Polarization encoding is performed by a self-compensating Sagnac loop modulator which exhibits high temporal stability and the lowest intrinsic quantum bit error rate reported so far.The QKD system was tested over a fiber-optic link, demonstrating tolerance up to about 40 dB of channel losses. Thanks to its reduced hardware requirements and the quality of the source, this work represents an important step towards technologically mature QKD systems., Comment: 8 pages, 4 figures

We propose Qubit4Sync, a synchronization method for Quantum Key Distribution (QKD) setups, based on the same qubits exchanged during the protocol and without requiring additional hardware other than the one necessary to prepare and measure the quantum states. Our approach introduces a new cross-correlation algorithm achieving the lowest computational complexity, to our knowledge, for high channel losses. We tested the robustness of our scheme in a real QKD implementation.

The future envisaged global-scale quantum communication network will comprise various nodes interconnected via optical fibers or free-space channels, depending on the link distance. The free-space segment of such a network should guarantee certain key requirements, such as daytime operation and the compatibility with the complementary telecom-based fiber infrastructure. In addition, space-to-ground links will require the capability of designing light and compact quantum devices to be placed in orbit. For these reasons, investigating available solutions matching all the above requirements is still necessary. Here we present a full prototype for daylight quantum key distribution at 1550 nm exploiting an integrated silicon-photonics chip as state encoder. We tested our prototype in the urban area of Padua (Italy) over a 145m-long free-space link, obtaining a quantum bit error rate around 0.5% and an averaged secret key rate of 30 kbps during a whole sunny day (from 11:00 to 20:00). The developed chip represents a cost-effective solution for portable free-space transmitters and a promising resource to design quantum optical payloads for future satellite missions.

The proposed mission "Space Atomic Gravity Explorer" (SAGE) has the scientific objective to investigate gravitational waves, dark matter, and other fundamental aspects of gravity as well as the connection between gravitational physics and quantum physics using new quantum sensors, namely, optical atomic clocks and atom interferometers based on ultracold strontium atoms., Comment: Published in Eur. Phys. J. D 73 (2019) 228 in the Topical Issue Quantum Technologies for Gravitational Physics, Guest editors Tanja Mehlstaubler, Yanbei Chen, Guglielmo M. Tino and Hsien-Chi Yeh

Entanglement is a fundamental resource for quantum information science. However, bipartite entanglement is destroyed when one particle is observed via projective (sharp) measurements, as it is typically the case in most experiments. Here we experimentally show that, if instead of sharp measurements, one performs many sequential unsharp measurements on one particle which are suitably chosen depending on the previous outcomes, then entanglement is preserved and it is possible to reveal quantum correlations through measurements on the second particle at any step of the sequence. Specifically, we observe that pairs of photons entangled in polarization maintain their entanglement when one particle undergoes three sequential measurements, and each of these can be used to violate a CHSH inequality. This proof-of-principle experiment demonstrates the possibility of repeatedly harnessing two crucial resources, entanglement and Bell nonlocality, that, in most quantum protocols, are destroyed after a single measurement. The protocol we use, which in principle works for an unbounded sequence of measurements, can be useful for randomness extraction.

Deployment of quantum technology in space provides opportunities for new types of precision tests of gravity. On the other hand, the operational demands of such technology can make previously unimportant effects practically relevant. We describe a novel optical interferometric red-shift measurement and a measurement scheme designed to witness possible spin-gravity coupling effects., Comment: 4 pages, 1 figure. Submitted to the Proceedings of the Fifteenth Marcel Grossmann Meeting, Rome, July 2018

Quantum cryptography is arguably the fastest growing area in quantum information science. Novel theoretical protocols are designed on a regular basis, security proofs are constantly improving, and experiments are gradually moving from proof-of-principle lab demonstrations to in-field implementations and technological prototypes. In this review, we provide both a general introduction and a state of the art description of the recent advances in the field, both theoretically and experimentally. We start by reviewing protocols of quantum key distribution based on discrete variable systems. Next we consider aspects of device independence, satellite challenges, and high rate protocols based on continuous variable systems. We will then discuss the ultimate limits of point-to-point private communications and how quantum repeaters and networks may overcome these restrictions. Finally, we will discuss some aspects of quantum cryptography beyond standard quantum key distribution, including quantum data locking and quantum digital signatures., Comment: Review article. Comments and suggestions are welcome. REVTeX: 118 pages, 20 figures, 785 references

Random numbers are a fundamental ingredient for many applications including simulation, modelling and cryptography. Sound random numbers should be independent and uniformly distributed. Moreover, for cryptographic applications they should also be unpredictable. We demonstrate a real-time self-testing source independent quantum random number generator (QRNG) that uses squeezed light as source. We generate secure random numbers by measuring the quadratures of the electromagnetic field without making any assumptions on the source; only the detection device is trusted. We use a homodyne detection to alternatively measure the Q and P conjugate quadratures of our source. Using the entropic uncertainty relation, measurements on P allow us to estimate a bound on the min-entropy of Q conditioned on any classical or quantum side information that a malicious eavesdropper may detain. This bound gives the minimum number of secure bits we can extract from the Q measurement. We discuss the performance of different estimators for this bound. We operate this QRNG with a squeezed state and we compare its performance with a QRNG using thermal states. The real-time bit rate was 8.2 kb/s when using the squeezed source and between 5.2-7.2 kb/s when the thermal state source was used., Comment: 11 pages, 9 figures

Quantum Key Distribution (QKD) allows distant parties to exchange cryptographic keys with unconditional security by encoding information on the degrees of freedom of photons. Polarization encoding has been extensively used in QKD implementations along free-space, optical fiber and satellite-based links. However, the polarization encoders used in such implementations are unstable, expensive, complex and can even exhibit side-channels that undermine the security of the implemented protocol. Here we propose a self-compensating polarization encoder based on a Lithium Niobate phase modulator inside a Sagnac interferometer and implement it using only standard telecommunication commercial off-the-shelves components (COTS). Our polarization encoder combines a simple design and high stability reaching an intrinsic quantum bit error rate as low as 0.2%. Since realization is possible from the 800 nm to the 1550 nm band by using COTS, our polarization modulator is a promising solution for free-space, fiber and satellite-based QKD., Comment: REVTeX, 5 pages, 4 figures

Satellite quantum communications have rapidly evolved in the past few years, culminating in the proposal, development, and deployment of satellite missions dedicated to quantum key distribution and the realization of fundamental tests of quantum mechanics in space. However, in comparison with the more mature technology based on fiber optics, several challenges are still open, such as the capability of detecting, with high temporal accuracy, single photons coming from orbiting terminals. Satellite laser ranging, commonly used to estimate satellite distance, could also be exploited to overcome this challenge. For example, high repetition rates and a low background noise can be obtained by determining the time-of-flight of faint laser pulses that are retro-reflected by geodynamics satellites and then detected on Earth at the single-photon level. Here we report an experiment with regard to achieving a temporal accuracy of approximately 230 ps in the detection of an optical signal of few photons per pulse reflected by satellites in medium Earth orbit, at a distance exceeding 7500 km, by using commercially available detectors. Lastly, the performance of the Matera Laser Ranging Observatory is evaluated in terms of the detection rate and the signal-to-noise ratio for satellite quantum communications., Comment: 7 pages, 4 figures, part of the "QUANTUM KEY DISTRIBUTION AND BEYOND" featured issue of the Journal of the Optical Society of America B

The versatility of silicon photonic integrated circuits has led to a widespread usage of this platform for quantum information based applications, including Quantum Key Distribution (QKD). However, the integration of simple high repetition rate photon sources is yet to be achieved. The use of weak-coherent pulses (WCPs) could represent a viable solution. For example, Measurement Device Independent QKD (MDI-QKD) envisions the use of WCPs to distill a secret key immune to detector side channel attacks at large distances. Thus, the integration of III-V lasers on silicon waveguides is an interesting prospect for quantum photonics. Here, we report the experimental observation of Hong-Ou-Mandel interference with 46\pm 2% visibility between WCPs generated by two independent III-V on silicon waveguide integrated lasers. This quantum interference effect is at the heart of many applications, including MDI-QKD. Our work represents a substantial first step towards an implementation of MDI-QKD fully integrated in silicon, and could be beneficial for other applications such as standard QKD and novel quantum communication protocols., Comment: 5 pages, 3 figures

The Einstein Equivalence Principle (EEP) underpins all metric theories of gravity. One of its key aspects is the local position invariance (LPI) of non-gravitational experiments, which is captured by the gravitational red-shift. The iconic gravitational red-shift experiment places two fermionic systems, used as clocks, in different gravitational potentials and compares them using the electromagnetic field. However, the electromagnetic field itself can be used as a clock, by comparing the phases acquired by two optical pulses propagating through different gravitational potentials. A fundamental point in the implementation of a satellite large-distance optical interferometric experiment is the suppression of the first-order Doppler effect, which dominates the weak gravitational signal necessary to test the EEP. Here, we propose a novel scheme to suppress it, by subtracting the phase-shifts measured in the one-way and in the two-way configuration between a ground station and a satellite. We present a detailed analysis of this technique within the post-Newtonian framework and perform some simulations of its performance using realistic satellite orbits and the state-of-the-art fiber technology at the telecom wavelength of 1550 nm., Comment: manuscript improved

Entanglement is an invaluable resource for fundamental tests of physics and the implementation of quantum information protocols such as device-independent secure communications. In particular, time-bin entanglement is widely exploited to reach these purposes both in free-space and optical fiber propagation, due to the robustness and simplicity of its implementation. However, all existing realizations of time-bin entanglement suffer from an intrinsic postselection loophole, which undermines their usefulness. Here, we report the first experimental violation of Bell's inequality with "genuine" time-bin entanglement, free of the postselection loophole. We introduced a novel function of the interferometers at the two measurement stations, that operate as fast synchronized optical switches. This scheme allowed to obtain a postselection-loophole-free Bell violation of more than nine standard deviations. Since our scheme is fully implementable using standard fiber-based components and is compatible with modern integrated photonics, our results pave the way for the distribution of genuine time-bin entanglement over long distances., Comment: RevTex

Satellite-based quantum communication is an invaluable resource for the realization of a quantum network at the global scale. In this regard, the use of satellites well beyond the low Earth orbits gives the advantage of long communication time with a ground station. However, high-orbit satellites pose a great technological challenge due to the high diffraction losses of the optical channel, and the experimental investigation of such quantum channels is still lacking. Here, we report on the first experimental exchange of single photons from Global Navigation Satellite System at a slant distance of 20000 kilometers, by exploiting the retroreflector array mounted on GLONASS satellites. We also observed the predicted temporal spread of the reflected pulses due to the geometrical shape of array. Finally, we estimated the requirements needed for an active source on a satellite, aiming towards quantum communication from GNSS with state-of-the-art technology., Comment: Revtex

New techniques based on weak measurements have recently been introduced to the field of quantum state reconstruction. Some of them allow the direct measurement of each matrix element of an unknown density operator and need only $O(d)$ different operations, compared to $d^2$ linearly independent projectors in the case of standard quantum state tomography, for the reconstruction of an arbitrary mixed state. However, due to the weakness of these couplings, these protocols are approximated and prone to large statistical errors. We propose a method which is similar to the weak measurement protocols but works regardless of the coupling strength: our protocol is not approximated and thus improves the accuracy and precision of the results with respect to weak measurement schemes. We experimentally apply it to the polarization state of single photons and compare the results to those of preexisting methods for different values of the coupling strength. Our results show that our method outperforms previous proposals in terms of accuracy and statistical errors., Comment: RevTex, 6 pages