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The power of quantum random number generation is more than just the ability to create truly random numbers$\unicode{x2013}$it can also enable self-testing, which allows the user to verify the implementation integrity of certain critical quantum components with minimal assumptions. In this work, we develop and implement a self-testing quantum random number generator (QRNG) chipset capable of generating 15.33 Mbits of certifiable randomness in each run (an expansion rate of $5.11\times 10^{-4}$ at a repetition rate of 10 Mhz). The chip design is based on a highly loss-and-noise tolerant measurement-device-independent protocol, where random coherent states encoded using quadrature phase shift keying are used to self-test the quantum homodyne detection unit: well-known to be challenging to characterise in practice. Importantly, this proposal opens up the possibility to implement miniaturised self-testing QRNG devices at production scale using standard silicon photonics foundry platforms., Comment: 15 Pages, 5 Figures, and 2 Tables

Liu et al. (ITCS22) initiated the study of designing a secure position verification protocol based on a specific proof of quantumness protocol and classical communication. In this paper, we study this interesting topic further and answer some of the open questions that are left in that paper. We provide a new generic compiler that can convert any single round proof of quantumness-based certified randomness protocol to a secure classical communication-based position verification scheme. Later, we extend our compiler to different kinds of multi-round proof of quantumness-based certified randomness protocols. Moreover, we instantiate our compiler with a random circuit sampling (RCS)-based certified randomness protocol proposed by Aaronson and Hung (STOC 23). RCS-based techniques are within reach of today's NISQ devices; therefore, our design overcomes the limitation of the Liu et al. protocol that would require a fault-tolerant quantum computer to realize. Moreover, this is one of the first cryptographic applications of RCS-based techniques other than certified randomness., Comment: v2: minor changes to related work and addition of acknowledgements. 54 pages, 10 figures, 1 table

Data privacy and authentication are two main security requirements for remote access and cloud services. While QKD has been explored to address data privacy concerns, oftentimes its use is separate from the client authentication protocol despite implicitly providing authentication. Here, we present a quantum authentication key expansion (QAKE) protocol that (1) integrates both authentication and key expansion within a single protocol, and (2) provides key recycling property -- allowing all authentication keys to be reused. We analyse the security of the protocol in a QAKE framework adapted from a classical authentication key exchange (AKE) framework, providing separate security conditions for authentication and data privacy. An experimental implementation of the protocol, with appropriate post-selection, was performed to demonstrate its feasibility., Comment: 71 pages, comments are welcome

We initiate the study of relativistic zero-knowledge quantum proof of knowledge systems with classical communication, formally defining a number of useful concepts and constructing appropriate knowledge extractors for all the existing protocols in the relativistic setting which satisfy a weaker variant of the special soundness property due to Unruh (EUROCRYPT 2012). We show that there exists quantum proofs of knowledge with knowledge error 1/2 + negl({\eta}) for all relations in NP via a construction of such a system for the Hamiltonian cycle relation using a general relativistic commitment scheme exhibiting the fairly-binding property due to Fehr and Fillinger (EUROCRYPT 2016). We further show that one can construct quantum proof of knowledge extractors for proof systems which do not exhibit special soundness, and therefore require an extractor to rewind multiple times. We develop a new multi-prover quantum rewinding technique by combining ideas from monogamy of entanglement and gentle measurement lemmas that can break the quantum rewinding barrier. Finally, we prove a new bound on the impact of consecutive measurements and use it to significantly improve the soundness bound of some existing relativistic zero knowledge proof systems, such as the one due to Chailloux and Leverrier (EUROCRYPT 2017)., Comment: 37 pages

In recent years, discrete-modulated continuous-variable quantum key distribution (DM-CV-QKD) has gained traction due to its practical advantages: cost-effectiveness, simple state preparation, and compatibility with existing communication technologies. This work presents a security analysis of DM-CV-QKD against general sequential attacks, including finite-size effects. Remarkably, our proof considers attacks that are neither independent nor identical, and makes no assumptions about the Hilbert space dimension of the receiver. To analyse the security, we leverage the recent generalised entropy accumulation theorem and the numerical methods based on quasi-relative entropy. We also develop a novel dimension reduction technique which is compatible with the entropy accumulation framework. While our analysis reveals significant finite-size corrections to the key rate, the protocol might still offer advantages in specific scenarios due to its practical merits. Our work also offers some insights on how future security proofs can improve the security bounds derived in this work., Comment: Updated the discussion section

We demonstrated for the first time quantum-safe high-speed 100 Gbps site-to-site IPsec tunnels secured using Quantum Key Distribution (QKD) technology. The demonstration was conducted between two JPMorgan Chase Data Centers (DCs) in an air-gapped environment over 46 km of deployed telecom fiber across Singapore achieving 45 days of continuous operation. Two different Virtual Private Network (VPN) tunnel configurations were tested: (1) a QKD-secured VPN tunnel configuration with a maximum throughput of 80 Gbps and (2) a multi-VPN tunnel configuration exhibiting 12 QKD-secured VPN tunnels with a throughput of 8.39 Gbps per tunnel resulting in an aggregated throughput of 99.62 Gbps for all tunnels. For the QKD system performance, we achieved an average Secret Key Rate (SKR) of 7.4 kbps (about 29 AES-256 keys per second), an average Quantum Bit Error Rate (QBER) of 0.8% and an average visibility of 98.6%. We utilized the ETSI-QKD-014 REST-based Application Programming Interface (API) to exchange the QKD generated keys between the key management server in the QKD system and the next-generation firewalls in order to encrypt and decrypt the data. The data was encrypted by the quantum-safe keys using the AES-256-GCM cipher suite with a key refresh rate of 120 seconds without affecting the VPN tunnel connectivity and performance, Comment: 7 pages, 4 figures, 1 table

Distributed quantum computing is a promising computational paradigm for performing computations that are beyond the reach of individual quantum devices. Privacy in distributed quantum computing is critical for maintaining confidentiality and protecting the data in the presence of untrusted computing nodes. In this work, we introduce novel blind quantum machine learning protocols based on the quantum bipartite correlator algorithm. Our protocols have reduced communication overhead while preserving the privacy of data from untrusted parties. We introduce robust algorithm-specific privacy-preserving mechanisms with low computational overhead that do not require complex cryptographic techniques. We then validate the effectiveness of the proposed protocols through complexity and privacy analysis. Our findings pave the way for advancements in distributed quantum computing, opening up new possibilities for privacy-aware machine learning applications in the era of quantum technologies., Comment: 11 pages, 3 figures

Randomness extraction is an essential post-processing step in practical quantum cryptography systems. When statistical fluctuations are taken into consideration, the requirement of large input data size could heavily penalise the speed and resource consumption of the randomness extraction process, thereby limiting the overall system performance. In this work, we propose a sampled sub-block hashing approach to circumvent this problem by randomly dividing the large input block into multiple sub-blocks and processing them individually. Through simulations and experiments, we demonstrate that our method achieves an order-of-magnitude improvement in system throughput while keeping the resource utilisation low. Furthermore, our proposed approach is applicable to a generic class of quantum cryptographic protocols that satisfy the generalised entropy accumulation framework, presenting a highly promising and general solution for high-speed post-processing in quantum cryptographic applications such as quantum key distribution and quantum random number generation., Comment: 15 pages, 8 figures. All comments are welcome

The coherent one-way (COW) quantum key distribution (QKD) is a highly practical quantum communication protocol that is currently deployed in off-the-shelves products. However, despite its simplicity and widespread use, the security of COW-QKD is still an open problem. This is largely due to its unique security feature based on inter-signal phase distribution, which makes it very difficult to analyze using standard security proof techniques. Here, to overcome this problem, we present a simple variant of COW-QKD and prove its security in the infinite-key limit. The proposed modifications only involve an additional vacuum tail signal following every encoded signal and a balanced beam-splitter for passive measurement basis choice. Remarkably, the resulting key rate of our protocol is comparable with both the existing upper-bound on COW-QKD key rate and the secure key rate of the coherent-state BB84 protocol. Our findings therefore suggest that the secured deployment of COW-QKD systems in high loss optical networks is indeed feasible with minimal adaptations applied to its hardware and software., Comment: 14 pages, 5 figures. All comments are welcome

In recent years, true random number generators (TRNGs) based on magnetic tunnelling junction (MTJ) have become increasingly attractive. This is because MTJ-based TRNGs offer some advantages over traditional CMOS-based TRNGs, such as smaller area and simpler structure. However, there has been no work thus far that quantified the quality of the raw output of an MTJ-based TRNG and performed suitable randomness extraction to produce provably-secure random bits, unlike their CMOS-based counterparts. In this work, we implement an MTJ-based TRNG and characterise the entropy of the raw output. Using this information, we perform post-processing to extract a set of random bits which are provably-secure., Comment: 6 pages, all comments are welcome

Device-independent quantum key distribution (DI-QKD) is often seen as the ultimate key exchange protocol in terms of security, as it can be performed securely with uncharacterised black-box devices. The advent of DI-QKD closes several loopholes and side-channels that plague current QKD systems. While implementing DI-QKD protocols is technically challenging, there have been recent proof-of-principle demonstrations, resulting from the progress made in both theory and experiments. In this review, we will provide an introduction to DI-QKD, an overview of the related experiments performed, and the theory and techniques required to analyse its security. We conclude with an outlook on future DI-QKD research., Comment: Review article, 47 pages, 3 figures. Accepted in Quantum

Quantum random number generators (QRNGs) are able to generate numbers that are certifiably random, even to an agent who holds some side-information. Such systems typically require that the elements being used are precisely calibrated and validly certified for a credible security analysis. However, this can be experimentally challenging and result in potential side-channels which could compromise the security of the QRNG. In this work, we propose, design and experimentally demonstrate a QRNG protocol that completely removes the calibration requirement for the measurement device. Moreover, our protocol is secure against quantum side-information. We also take into account the finite-size effects and remove the independent and identically distributed requirement for the measurement side. More importantly, our QRNG scheme features a simple implementation which uses only standard optical components and are readily implementable on integrated-photonic platforms. To validate the feasibility and practicability of the protocol, we set up a fibre-optical experimental system with a home-made homodyne detector with an effective efficiency of 91.7% at 1550nm. The system works at a rate of 2.5MHz, and obtains a net randomness expansion rate of 4.98kbits/s at 1E10 rounds. Our results pave the way for an integrated QRNG with self-testing feature and provable security., Comment: This is a preliminary draft, comments and suggestions are welcomed!

Device-independent quantum key distribution (DIQKD) is the art of using untrusted devices to establish secret keys over an untrusted channel. So far, the real-world implementation of DIQKD remains a major challenge, as it requires the demonstration of a loophole-free Bell test across two remote locations with very high quality entanglement to ensure secure key exchange. Here, we demonstrate for the first time the distribution of a secure key -- based on asymptotic security estimates -- in a fully device-independent way between two users separated by 400 metres. The experiment is based on heralded entanglement between two independently trapped single Rubidium 87 atoms. The implementation of a robust DIQKD protocol indicates an expected secret key rate of r=0.07 per entanglement generation event and r>0 with a probability error of 3%. Furthermore, we analyse the experiment's capability to distribute a secret key with finite-size security against collective attacks., Comment: 16 pages

Secure information retrieval is an essential task in today's highly digitised society. In some applications, it may be necessary that user query's privacy and database content's security are enforced. For these settings, symmetric private information retrieval (SPIR) could be employed, but its implementation is known to be demanding, requiring a private key-exchange network as the base layer. Here, we report for the first time a realisation of provably-secure SPIR supported by a quantum-secure key-exchange network. The SPIR scheme looks at biometric security, offering secure retrieval of 582-byte fingerprint files from a database with 800 entries. Our experimental results clearly demonstrate the feasibility of SPIR with quantum secure communications, thereby opening up new possibilities in secure distributed data storage and cloud computing over the future Quantum Internet.

Most quantum key distribution (QKD) protocols can be classified as either a discrete-variable (DV) protocol or continuous-variable (CV) protocol, based on how classical information is being encoded. We propose a protocol that combines the best of both worlds -- the simplicity of quantum state preparation in DV-QKD together with the cost-effective and high-bandwidth of homodyne detectors used in CV-QKD. Our proposed protocol has two highly practical features: (1) it does not require the honest parties to share the same reference phase (as required in CV-QKD) and (2) the selection of decoding basis can be performed after measurement. We also prove the security of the proposed protocol in the asymptotic limit under the assumption of collective attacks. Our simulation suggests that the protocol is suitable for secure and high-speed practical key distribution over metropolitan distances., Comment: Updated the format to Quantum article. 11 pages of main text + 4 pages of Appendices, 3 figures

Characterising the input-output photon-number distribution of an unknown optical quantum channel is an important task for many applications in quantum information processing. Ideally, this would require deterministic photon-number sources and photon-number-resolving detectors, but these technologies are still work-in-progress. In this work, we propose a general method to rigorously bound the input-output photon number distribution of an unknown optical channel using standard optical devices such as coherent light sources and non-photon-number-resolving detectors/homodyne detectors. To demonstrate the broad utility of our method, we consider the security analysis of practical quantum key distribution systems based on calibrated single-photon detectors and an experimental proposal to implement time-correlated single photon counting technology using homodyne detectors instead of single-photon detectors., Comment: 19 pages, 7 figures

The security of finite-length keys is essential for the implementation of device-independent quantum key distribution (DIQKD). Presently, there are several finite-size DIQKD security proofs, but they are mostly focused on standard DIQKD protocols and do not directly apply to the recent improved DIQKD protocols based on noisy preprocessing, random key measurements, and modified CHSH inequalities. Here, we provide a general finite-size security proof that can simultaneously encompass these approaches, using tighter finite-size bounds than previous analyses. In doing so, we develop a method to compute tight lower bounds on the asymptotic keyrate for any such DIQKD protocol with binary inputs and outputs. With this, we show that positive asymptotic keyrates are achievable up to depolarizing noise values of $9.33\%$, exceeding all previously known noise thresholds. We also develop a modification to random-key-measurement protocols, using a pre-shared seed followed by a "seed recovery" step, which yields substantially higher net key generation rates by essentially removing the sifting factor. Some of our results may also improve the keyrates of device-independent randomness expansion., Comment: Corrected error in Chernoff bound formula

Controlling the energy of unauthorized light signals in a quantum cryptosystem is an essential criterion for implementation security. Here, we propose a passive optical power limiter device based on thermo-optical defocusing effects providing a reliable power limiting threshold which can be readily adjusted to suit various quantum applications. In addition, the device is robust against a wide variety of signal variations (e.g. wavelength, pulse width), which is important for implementation security. Moreover, we experimentally show that the proposed device does not compromise quantum communication signals, in that it has only a very minimal impact (if not, negligible impact) on the intensity, phase, or polarization degrees of freedom of the photon, thus making it suitable for general communication purposes. To show its practical utility for quantum cryptography, we demonstrate and discuss three potential applications: (1) measurement-device-independent quantum key distribution with enhanced security against a general class of Trojan-horse attacks, (2) using the power limiter as a countermeasure against bright illumination attacks, and (3) the application of power limiters to potentially enhance the implementation security of plug-and-play quantum key distribution.

The security of real-world quantum key distribution (QKD) critically depends on the number of data points the system can collect in a fixed time interval. To date, state-of-the-art finite-key security analyses require block lengths in the order of 1E4 bits to obtain positive secret keys. This requirement, however, can be very difficult to achieve in practice, especially in the case of entanglement-based satellite QKD systems, where the overall channel loss can go up to 70 dB or more. Here, we provide an improved finite-key security analysis which can reduce the block length requirement by 14% to 17% for standard channel and protocol settings. In practical terms, this reduction could save entanglement-based satellite QKD weeks of measurement time and resources, thereby bringing space-based QKD technology closer to reality. As an application, we use the improved analysis to show that the recently reported Micius QKD satellite is capable of generating positive secret keys with a $1E-5$ security level., Comment: Revised draft; 5 pages, 1 figure. We warmly welcome comments/corrections, as well as suggestions for additional areas to study

The security of measurement device-independent quantum key distribution (MDI QKD) relies on a thorough characterization of one's optical source output, especially any noise in the state preparation process. Here, we provide an extension of the loss-tolerant protocol [Phys. Rev. A 90, 052314 (2014)], a leading proof technique for analyzing the security of QKD, to MDI QKD protocols that employ mixed signal states. We first reframe the core of the proof technique, noting its generalization to treat $d$-dimensional signal encodings. Concentrating on the qubit signal state case, we find that the mixed states can be interpreted as providing Alice and Bob with a virtual shield system they can employ to reduce Eve's knowledge of the secret key. We then introduce a simple semidefinite programming method for optimizing the virtual operations they can perform on the shield system to yield a higher key rate, along with an example calculation of fundamentally achievable key rates in the case of random polarization modulation error., Comment: 15 pages, 3 figures (including supplementary materials). Comments welcome

Device-independent quantum key distribution (DIQKD) is the art of using untrusted devices to distribute secret keys in an insecure network. It thus represents the ultimate form of cryptography, offering not only information-theoretic security against channel attacks, but also against attacks exploiting implementation loopholes. In recent years, much progress has been made towards realising the first DIQKD experiments, but current proposals are just out of reach of today's loophole-free Bell experiments. Here, we significantly narrow the gap between the theory and practice of DIQKD with a simple variant of the original protocol based on the celebrated Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. By using two randomly chosen key generating bases instead of one, we show that our protocol significantly improves over the original DIQKD protocol, enabling positive keys in the high noise regime for the first time. We also compute the finite-key security of the protocol for general attacks, showing that approximately 1E8 to 1E10 measurement rounds are needed to achieve positive rates using state-of-the-art experimental parameters. Our proposed DIQKD protocol thus represents a highly promising path towards the first realisation of DIQKD in practice., Comment: 22 pages;Main article (10 pages); Supplementary Information (12 pages)

Private information retrieval (PIR) is a database query protocol that provides user privacy, in that the user can learn a particular entry of the database of his interest but his query would be hidden from the data centre. Symmetric private information retrieval (SPIR) takes PIR further by additionally offering database privacy, where the user cannot learn any additional entries of the database. Unconditionally secure SPIR solutions with multiple databases are known classically, but are unrealistic because they require long shared secret keys between the parties for secure communication and shared randomness in the protocol. Here, we propose using quantum key distribution (QKD) instead for a practical implementation, which can realise both the secure communication and shared randomness requirements. We prove that QKD maintains the security of the SPIR protocol and that it is also secure against any external eavesdropper. We also show how such a classical-quantum system could be implemented practically, using the example of a two-database SPIR protocol with keys generated by measurement device-independent QKD. Through key rate calculations, we show that such an implementation is feasible at the metropolitan level with current QKD technology., Comment: 19 pages

Device-independent quantum key distribution (DIQKD) provides the strongest form of secure key exchange, using only the input-output statistics of the devices to achieve information-theoretic security. Although the basic security principles of DIQKD are now well-understood, it remains a technical challenge to derive reliable and robust security bounds for advanced DIQKD protocols that go beyond the previous results based on violations of the CHSH inequality. In this work, we present a framework based on semi-definite programming that gives reliable lower bounds on the asymptotic secret key rate of any QKD protocol using untrusted devices. In particular, our method can in principle be utilized to find achievable secret key rates for any DIQKD protocol, based on the full input-output probability distribution or any choice of Bell inequality. Our method also extends to other DI cryptographic tasks., Comment: Improved proof of strong duality. Close to published version

Fiber-based quantum communication networks are currently limited without quantum repeaters. Satellite-based quantum links have been proposed to extend the network domain. We have developed a quantum communication system, suitable for realistic satellite-to-ground communication. With this system, we have executed an entanglement-based quantum key distribution (QKD) protocol developed by Bennett, Brassard, and Mermin in 1992 (BBM92), achieving quantum bit error rates (QBER) below 2$\%$ in all bases. More importantly, we demonstrate low QBER execution of a higher dimensional hyperentanglement-based QKD protocol, using photons simultaneously entangled in polarization and time-bin, leading to significantly higher secure key rates, at the cost of increased technical complexity and system size. We show that our protocol is suitable for a space-to-ground link, after incorporating Doppler shift compensation, and verify its security using a rigorous finite-key analysis. Additionally, We discuss system engineering considerations relevant to those and other quantum communication protocols, and their dependence on what photonic degrees of freedom are utilized., Comment: 30 pages, 11 figures, and 4 tables

Quantum key distribution (QKD) based on coherent states is well known for its implementation simplicity, but it suffers from loss-dependent attacks based on optimal unambiguous state discrimination. Crucially, previous research has suggested that coherent-state QKD is limited to short distances, typically below 100 km assuming standard optical fiber loss and system parameters. In this work, we propose a six-coherent-state phase-encoding QKD protocol that is able to tolerate the total loss of up to 38 dB assuming realistic system parameters, and up to 56 dB loss assuming zero noise. The security of the protocol is calculated using a recently developed security proof technique based on semi-definite programming, which assumes only the inner-product information of the encoded coherent states, the expected statistics, and that the measurement is basis-independent. Our results thus suggest that coherent-state QKD could be a promising candidate for high-speed provably-secure QKD., Comment: 8 pages; 6 figures

We derive a sufficient condition for advantage distillation to be secure against collective attacks in device-independent quantum key distribution (DIQKD), focusing on the repetition-code protocol. In addition, we describe a semidefinite programming method to check whether this condition holds for any probability distribution obtained in a DIQKD protocol. Applying our method to various probability distributions, we find that advantage distillation is possible up to depolarising-noise values of $q \approx 9.1\%$ or limited detector efficiencies of $\eta \approx 89.1\%$ in a 2-input 2-output scenario. This exceeds the noise thresholds of $q \approx 7.1\%$ and $\eta \approx 90.7\%$ respectively for DIQKD with one-way error correction using the CHSH inequality, thereby showing that it is possible to distill secret key beyond those thresholds., Comment: [v2] Corrected threshold detection efficiency for one-way error correction, reorganised material. [v3] Updated funding information

It is well-known that no local model - in theory - can simulate the outcome statistics of a Bell-type experiment as long as the detection efficiency is higher than a threshold value. For the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality this theoretical threshold value is $\eta_{\text{T}} = 2 (\sqrt{2}-1) \approx 0.8284$. On the other hand, Phys.\ Rev.\ Lett.\ 107, 170404 (2011) outlined an explicit practical model that can fake the CHSH inequality for a detection efficiency of up to $0.5$. In this work, we close this gap. More specifically, we propose a method to emulate a Bell inequality at the threshold detection efficiency using existing optical detector control techniques. For a Clauser-Horne-Shimony-Holt inequality, it emulates the CHSH violation predicted by quantum mechanics up to $\eta_{\text{T}}$. For the Garg-Mermin inequality - re-calibrated by incorporating non-detection events - our method emulates its exact local bound at any efficiency above the threshold. This confirms that attacks on secure quantum communication protocols based on Bell violation is a real threat if the detection efficiency loophole is not closed., Comment: 7 pages, 3 figures

We propose and experimentally demonstrate a new scheme for measuring high-dimensional phase states using a two-photon interference technique, which we refer to as quantum-controlled measurement. Using this scheme, we implement a $d$-dimensional time-phase quantum key distribution (QKD) system and achieve secret key rates of 5.26 and 8.65 Mbps using $d = 2$ and $d = 8$ quantum states, respectively, for a 4~dB channel loss, illustrating that high-dimensional time-phase QKD protocols are advantageous for low-loss quantum channels. This work paves the way for practical high-dimensional QKD protocols for metropolitan-scale systems. Furthermore, our results apply equally well for other high-dimensional protocols, such as those using the spatial degree-of-freedom with orbital angular momentum states being one example., Comment: published version

Measurement-device-independent quantum key distribution (MDI-QKD) is the only known QKD scheme that can completely overcome the problem of detection side-channel attacks. Yet, despite its practical importance, there is no standard approach towards proving the security of MDI-QKD. Here, we present a simple numerical method that can efficiently compute almost-tight security bounds for any discretely modulated MDI-QKD protocol. To demonstrate the broad utility of our method, we use it to analyze the security of coherent-state MDI-QKD, decoy-state MDI-QKD with leaky sources, and a variant of twin-field QKD called phase-matching QKD. In all of the numerical simulations (using realistic detection models) we find that our method gives significantly higher secret key rates than those obtained with current security proof techniques. Interestingly, we also find that phase-matching QKD using only two coherent test states is enough to overcome the fundamental rate-distance limit of QKD. Taken together, these findings suggest that our security proof method enables a versatile, fast, and possibly optimal approach towards the security validation of practical MDI-QKD systems., Comment: 15 pages, 6 figures. Title has been revised

Prepare-and-measure (P&M) quantum networks are the basic building blocks of quantum communication and cryptography. These networks crucially rely on non-orthogonal quantum encodings to distribute quantum correlations, thus enabling superior communication rates and information-theoretic security. Here, we present a computational toolbox that is able to efficiently characterise the set of input-output probability distributions for any discrete-variable P&M quantum network, assuming only the inner-product information of the quantum encodings. Our toolbox is thus highly versatile and can be used to analyse a wide range of quantum network protocols, including those that employ infinite-dimensional quantum code states. To demonstrate the feasibility and efficacy of our toolbox, we use it to reveal new results in multipartite quantum distributed computing and quantum cryptography. Taken together, these findings suggest that our method may have implications for quantum network information theory and the development of new quantum technologies., Comment: This version includes a new security analysis of coherent-one way quantum key distribution; Title and introduction have also been revised; Added new co-author (Emilien Lavie)

We propose a new method for implementing mutually unbiased generation and measurement of time-bin qudits using a cascade of electro-optic phase modulator -- coded fiber Bragg grating pairs. Our approach requires only a single spatial mode and can switch rapidly between basis choices. We obtain explicit solutions for dimensions $d=2,3,4$ that realize all $d+1$ possible mutually unbiased bases and analyze the performance of our approach in quantum key distribution. Given its practicality and compatibility with current technology, our approach provides a promising springboard for scalable processing of high-dimensional time-bin states., Comment: 11 pages, 12 figures

Quantum key distribution (QKD) allows two remote users to establish a secret key in the presence of an eavesdropper. The users share quantum states prepared in two mutually-unbiased bases: one to generate the key while the other monitors the presence of the eavesdropper. Here, we show that a general $d$-dimension QKD system can be secured by transmitting only a subset of the monitoring states. In particular, we find that there is no loss in the secure key rate when dropping one of the monitoring states. Furthermore, it is possible to use only a single monitoring state if the quantum bit error rates are low enough. We apply our formalism to an experimental $d=4$ time-phase QKD system, where only one monitoring state is transmitted, and obtain a secret key rate of $17.4 \pm 2.8$ Mbits/s at a 4 dB channel loss and with a quantum bit error rate of $0.045\pm0.001$ and $0.044\pm0.001$ in time and phase bases, respectively, which is 58.4 % of the secret key rate that can be achieved with the full setup. This ratio can be increased, potentially up to 100 %, if the error rates in time and phase basis are reduced. Our results demonstrate that it is possible to substantially simplify the design of high-dimension QKD systems, including those that use the spatial or temporal degrees-of-freedom of the photon, and still outperform qubit-based ($d = 2$) protocols.

The security of conventional cryptography systems is threatened in the forthcoming era of quantum computers. Quantum key distribution (QKD) features fundamentally proven security and offers a promising option for quantum-proof cryptography solution. Although prototype QKD systems over optical fiber have been demonstrated over the years, the key generation rates remain several orders-of-magnitude lower than current classical communication systems. In an effort towards a commercially viable QKD system with improved key generation rates, we developed a discrete-variable QKD system based on time-bin quantum photonic states that is capable of generating provably-secure cryptographic keys at megabit-per-second (Mbps) rates over metropolitan distances. We use high-dimensional quantum states that transmit more than one secret bit per received photon, alleviating detector saturation effects in the superconducting nanowire single-photon detectors (SNSPDs) employed in our system that feature very high detection efficiency (of over 70%) and low timing jitter (of less than 40 ps). Our system is constructed using commercial off-the-shelf components, and the adopted protocol can readily be extended to free-space quantum channels. The security analysis adopted to distill the keys ensures that the demonstrated protocol is robust against coherent attacks, finite-size effects, and a broad class of experimental imperfections identified in our system.

The robust estimation of entanglement is key to the validation of implementations of quantum systems. On the one hand, the evaluation of standard entanglement measures, either using quantum tomography or using quantitative entanglement witnesses requires perfect implementation of measurements. On the other hand, measurement-device-independent entanglement witnesses (MDIEWs) can certify entanglement of all entangled states using untrusted measurement devices. We show that MDIEWs can be used as well to quantify entanglement according to standard entanglement measures, and present a practical method to derive such witnesses using experimental data only., Comment: Close to published version. 15 pages incl. 5 pages Appendix, 3 figures

Recently, we proposed a simultaneous quantum and classical communication (SQCC) protocol, where random numbers for quantum key distribution (QKD) and bits for classical communication are encoded on the \emph{same} weak coherent pulse, and decoded by the \emph{same} coherent receiver. Such a scheme could be appealing in practice since a single coherent communication system can be used for multiple purposes. However, previous studies show that the SQCC protocol can only tolerate very small phase noise. This makes it incompatible with the coherent communication scheme using a true local oscillator (LO), which presents a relatively high phase noise due to the fact that the signal and the LO are generated from two independent lasers. In this paper, we improve the phase noise tolerance of the SQCC scheme using a true LO by adopting a refined noise model where phase noises originated from different sources are treated differently: on one hand, phase noise associated with the coherent receiver may be regarded as \emph{trusted} noise, since the detector can be calibrated locally and the photon statistics of the detected signals can be determined from the measurement results; on the other hand, phase noise due to the instability of fiber interferometers may be regarded as \emph{untrusted} noise, since its randomness (from the adversary's point to view) is hard to justify. Simulation results show the tolerable phase noise in this refined noise model is significantly higher than that in the previous study where all the phase noises are assumed to be untrusted. We conduct an experiment to show the required phase stability can be achieved in a coherent communication system using a true LO., Comment: 10 pages, 6 figures

Several quantum key distribution (QKD) protocols employ iterative sifting. After each quantum transmission round, Alice and Bob disclose part of their setting information (including their basis choices) for the detected signals. The quantum phase of the protocol then ends when the numbers of detected signals per basis exceed certain pre-agreed threshold values. Recently, however, Pfister et al. [New J. Phys. 18 053001 (2016)] showed that iterative sifting makes QKD insecure, especially in the finite key regime, if the parameter estimation for privacy amplification uses the random sampling theory. This implies that a number of existing finite key security proofs could be flawed and cannot guarantee security. Here, we solve this serious problem by showing that the use of Azuma's inequality for parameter estimation makes QKD with iterative sifting secure again. This means that the existing protocols whose security proof employs this inequality remain secure even if they employ iterative sifting. Also, our results highlight a fundamental difference between the random sampling theorem and Azuma's inequality in proving security., Comment: 9 pages. We have found a flaw in the first version, which we have corrected in the revised version

Quantum position verification (QPV) is the art of verifying the geographical location of an untrusted party. Recently, it has been shown that the widely studied Bennett & Brassard 1984 (BB84) QPV protocol is insecure after the 3 dB loss point assuming local operations and classical communication (LOCC) adversaries. Here, we propose a time-reversed entanglement swapping QPV protocol (based on measurement-device-independent quantum cryptography) that is highly robust against quantum channel loss. First, assuming ideal qubit sources, we show that the protocol is secure against LOCC adversaries for any quantum channel loss, thereby overcoming the 3 dB loss limit. Then, we analyze the security of the protocol in a more practical setting involving weak laser sources and linear optics. In this setting, we find that the security only degrades by an additive constant and the protocol is able to verify positions up to 47 dB channel loss., Comment: 11 pages, 3 figures. Partially based on an earlier work in arXiv:1510.04891

One of the most pressing issues in quantum key distribution (QKD) is the problem of detector side- channel attacks. To overcome this problem, researchers proposed an elegant "time-reversal" QKD protocol called measurement-device-independent QKD (MDI-QKD), which is based on time-reversed entanglement swapping. However, MDI-QKD is more challenging to implement than standard point- to-point QKD. Recently, an intermediary QKD protocol called detector-device-independent QKD (DDI-QKD) has been proposed to overcome the drawbacks of MDI-QKD, with the hope that it would eventually lead to a more efficient detector side-channel-free QKD system. Here, we analyze the security of DDI-QKD and elucidate its security assumptions. We find that DDI-QKD is not equivalent to MDI-QKD, but its security can be demonstrated with reasonable assumptions. On the more practical side, we consider the feasibility of DDI-QKD and present a fast experimental demonstration (clocked at 625 MHz), capable of secret key exchange up to more than 90 km., Comment: 9 pages, 4 figures

Quantum nonlocality is a counterintuitive phenomenon that lies beyond the purview of causal influences. Recently, Bell inequalities have been generalized to the case of quantum inputs, leading to a powerful family of semi-quantum Bell inequalities that are capable of detecting any entangled state. Here, we focus on a different problem and investigate how the local-indistinguishability of quantum inputs and postselection may affect the requirements to detect semi-quantum nonlocality. To this end, we consider a semi-quantum nonlocal game based on locally-indistinguishable qubit inputs and derive its postselected local and quantum bounds by using a novel connection to the local-distinguishability of quantum states. Interestingly, we find that the postselected local bound is independent of the measurement efficiency and that the Bell violation increases with lower measurement efficiencies., Comment: 8 pages + 3 figures. Presented in the 1st International Workshop on Trustworthy Quantum Information, 6/28-7/2, University of Michigan, Ann Arbor, Michigan, US; Similar to published version (references to quantum steering added)

We propose a free-space reconfigurable quantum key distribution (QKD) network to secure communication among mobile users. Depends on the trustworthiness of the network relay, the users can implement either the highly secure measurement-device-independent QKD, or the highly efficient decoy state BB84 QKD. Based on the same quantum infrastructure, we also propose a loss tolerant quantum position verification scheme, which could allow the QKD users to initiate the QKD process without relying on pre-shared key., Comment: Submitted to IEEE The International Conference on Space Optical Systems and Applications (ICSOS) 2015

In recent years, the gap between theory and practice in quantum key distribution (QKD) has been significantly narrowed, particularly for QKD systems with arbitrarily awed optical receivers. The status for QKD systems with imperfect light sources is however less satisfactory, in the sense that the resulting secure key rates are often overly-dependent on the quality of state preparation. This is especially the case when the channel loss is high. Very recently, to overcome this limitation, Tamaki et al proposed a QKD protocol based on the so-called rejected data analysis, and showed that its security|in the limit of infinitely long keys|is almost independent of any encoding flaw in the qubit space, being this protocol compatible with the decoy state method. Here, as a step towards practical QKD, we show that a similar conclusion is reached in the finite-key regime, even when the intensity of the light source is unstable. More concretely, we derive security bounds for a wide class of realistic light sources and show that the bounds are also efficient in the presence of high channel loss. Our results strongly suggest the feasibility of long distance provably-secure communication with imperfect light sources., Comment: 27 pages, 7 figures