Continuous-variable (CV) quantum key distribution (QKD) allows for quantum secure communication with the benefit of being close to classical coherent communication. In recent years, CV QKD protocols using a discrete number of displaced coherent states have been studied intensively as the modulation can be directly implemented with real devices with finite resolution. Until now, experiments only calculated key rates in the asymptotic regime. Here, we present a CV QKD system using discrete modulation that is especially designed for atmospheric channels. We use polarization encoding to exploit the nonbirefringent nature of the turbulent atmosphere. This allows to expand CV QKD networks beyond the existing fiber backbone. In a laboratory demonstration with a static 3-decibel loss channel, we implemented a recently developed security proof allowing to calculate composable finite-size key rates against independently and identically distributed collective attacks. We applied the full QKD protocol including a quantum random number generator, error correction, and privacy amplification to extract secret keys.

Pre-shared keys (PSK) have been widely used in network security. Nonetheless, existing PSK solutions are not scalable. Moreover, whenever a new user joins a network, PSK requires an existing user to get a new key before they are able to communicate with the new user. The key issue is how to distribute the PSK between different users. Here, we solve this problem by proposing a new protocol called Distributed Symmetric Key Establishment (DSKE)(1). DSKE has the advantage of being scalable. Unlike standard public key infrastructure (PKI) which relies on computational assumptions, DSKE provides information-theoretic security in a universally composable security framework. Specifically, we prove the security (correctness and confidentiality) and robustness of this protocol against a computationally unbounded adversary, who additionally may have fully compromised a bounded number of the intermediaries and can eavesdrop on all communication. DSKE also achieves distributed trust through secret sharing. We present several implementations of DSKE in real environments, such as providing client services to link encryptors, network encryptors, and mobile phones, as well as the implementation of intermediaries, called Security Hubs, and associated test data as evidence for its versatility. As DSKE is highly scalable in a network setting with no distance limit, it is expected to be a cost-effective quantum-safe cryptographic solution to the network security threat presented by quantum computers.

In our work, we developed an optical CVQKD system that uses polarization-based QPSK modulation designed for atmospheric quantum communication and a corresponding post-processing pipeline including error correction and privacy amplification. In a first laboratory experiment, we applied the security statement of a recently published security proof to calculate composable key rates with a total security parameter of ε = 1e-10 in the finite size regime against i.i.d. collective attacks. We also used the post-processing pipeline to study the effect of error correction and frame errors on the actual key extraction in a finite-size system – finding that the common approach of going to high frame errors to increase the ECC efficiency β does not optimize the extractable key length.Furthermore, we deployed the system over an ad-hoc atmospheric channel of 1.7 km in Mai 2023 in the city of Jena, Germany. In a first proof-of-principle study, we were able to apply the full optical and post-processing pipeline to extract pseudo-asymptotic keys and discuss the further steps necessary to move the system to the finite-size regime. To the best of our knowledge, this is the first CVQKD demonstration over a real atmospheric channel combining both the new class of DMCVQKD security proofs without Gaussian optimality and error correction steps.

An important goal in quantum key distribution (QKD) is the task of providing a finite-size security proof without the assumption of collective attacks. For prepare-and-measure QKD, one approach for obtaining such proofs is the generalized entropy-accumulation theorem (GEAT) but thus far it has only been applied to study a small selection of protocols. In this work, we present techniques for applying the GEAT in finite-size analysis of generic prepare-and-measure protocols, with a focus on decoy-state protocols. In particular, we present an improved approach for computing entropy bounds for decoy-state protocols, which has the dual benefits of providing tighter bounds than previous approaches (even asymptotically) and being compatible with methods for computing min-trade-off functions in the GEAT. Furthermore, we develop methods to incorporate some improvements to the finite-size terms in the GEAT and implement techniques to automatically optimize the min-trade-off function. Our approach also addresses some numerical-stability challenges specific to prepare-and-measure protocols, which have not been addressed in previous works.

Besides discrete-variable QKD, where single photon detection is used, continuous-variable (CV) protocols are using homodyne detection and are thus promising to be compatible with existing classical coherent communication technology. Originally, the research on CV QKD protocols mostly focused on Gaussian modulation (see review [1]), where one assumes that Alice can continuously displace coherent states according to a 2D Gaussian distribution. This modulation allows the security proofs to take advance of Gaussian optimality conditions, but experimental implementations can only reach this pattern up to some finite discretization. Another approach is to directly use a discrete-modulated (DM) CV QKD protocol. Here, Alice is required to prepare a finite number of displaced coherent states, aiming for a higher experimental simplicity, with the drawback of higher theoretical complexity. Recently, new security proofs such as [2] and corresponding experiments [3,4] could show the feasibility of systems using quadrature amplitude modulation (QAM) with 64 and 256 displaced states. However, the security proof was limited to the asymptotic regime and since the experiments did not use implemented error correction codes, one could only estimate the achievable key rates, but could not generate the secret key itself. In this poster, we demonstrate experiments with a protocol with a smaller constellation size of four coherent states that share the same amplitude but are shifted by 90° in phase (QPSK modulation). We exploit a recently published security proof providing tight secret key rates for collective attacks even in the finite size regime [5]. Furthermore, we show that the QPSK data is compatible with our implemented low density parity check (LDPC) codes for binary symmetric channels. This allows us to perform the full QKD protocol from experimental quantum state exchange to classical post processing and to generate a secret key shared between Alice and Bob. For this purpose, we use a laboratory system based on polarization encoding in the Stokes parameters which is equivalent to a QPSK pattern in phase space. This scheme is designed to cope with the challenges of a turbulent atmospheric channel. While the fluctuating nature of such a channel can be targeted by sub-binning the transmission channels [6], the atmosphere is in general non-birefringent, allowing for atmospheric quantum communications [7]. [1] F. Laudenbach et al., Adv. Quantum Technol. 1, 1800011 (2018) [2] A. Denys et al., Quantum 5, 540 (2021) [3] F. Roumestan et al., arXiv:2207.11702 (2022) [4] Y. Pan et al., Optics Letters 47, 3307-3310 (2022) [5] F. Kanitschar et al., arXiv:2301.08686v1 (2023) [6] V. Usenko et al., New J. Phys. 14, 093048 (2012) [7] B. Heim et al., New J. Phys. 16, 113018 (2014)

Discrete-Modulated (DM) Continuous-Variable Quantum Key Distribution (CV-QKD) protocols are promising candidates for commercial implementations of quantum communication networks due to their experimental simplicity. While tight security analyses in the asymptotic limit exist, proofs in the finite-size regime are still subject to active research. We present a composable finite-size security proof against independently and identically distributed collective attacks for a general DM CV-QKD protocol. We introduce a new energy testing theorem to bound the effective dimension of Bob's system and rigorously prove security within Renner's epsilon-security framework and address the issue of acceptance sets in protocols and their security proof. We want to highlight, that our method also allows for nonunique acceptance statistics, which is necessary in practise. Finally, we extend and apply a numerical security proof technique to calculate tight lower bounds on the secure key rate. To demonstrate our method, we apply it to a quadrature phase-shift keying protocol, both for untrusted, ideal and trusted nonideal detectors. The results show that our security proof method yields secure finite-size key rates under experimentally viable conditions up to at least 72km transmission distance.

Security proof methods for quantum key distribution, QKD, that are based on the numerical key rate calculation problem, are powerful in principle. However, the practicality of the methods are limited by computational resources and the efficiency and accuracy of the underlying algorithms for convex optimization. We derive a stable reformulation of the convex nonlinear semidefinite programming, SDP, model for the key rate calculation problems. We use this to develop an efficient, accurate algorithm. The stable reformulation is based on novel forms of facial reduction, FR, for both the linear constraints and nonlinear quantum relative entropy objective function. This allows for a Gauss-Newton type interior-point approach that avoids the need for perturbations to obtain strict feasibility, a technique currently used in the literature. The result is high accuracy solutions with theoretically proven lower bounds for the original QKD from the FR stable reformulation. This provides novel contributions for FR for general SDP. We report on empirical results that dramatically improve on speed and accuracy, as well as solving previously intractable problems.

The Entropy Accumulation Theorem (EAT) was introduced to significantly improve the finite-size rates for device-independent quantum information processing tasks such as device-independent quantum key distribution (QKD). A natural question would be whether it also improves the rates for device-dependent QKD. In this work, we provide an affirmative answer to this question. We present new tools for applying the EAT in the device-dependent setting. We present sufficient conditions for the Markov chain conditions to hold as well as general algorithms for constructing the needed min-tradeoff function. Utilizing Dupuis' recent privacy amplification without smoothing result, we improve the key rate by optimizing the sandwiched Rényi entropy directly rather than considering the traditional smooth min-entropy. We exemplify these new tools by considering several examples including the BB84 protocol with the qubit-based version and with a realistic parametric down-conversion source, the six-state four-state protocol and a high-dimensional analog of the BB84 protocol.

We develop a method to connect the infinite-dimensional description of optical continuous-variable quantum key distribution (QKD) protocols to a finite-dimensional formulation. The secure key rates of the optical QKD protocols can then be evaluated using recently-developed reliable numerical methods for key rate calculations. We apply this method to obtain asymptotic key rates for discrete-modulated continuous-variable QKD protocols, which are of practical significance due to their experimental simplicity and potential for large-scale deployment in quantum-secured networks. Importantly, our security proof does not require the photon-number cutoff assumption relied upon in previous works. We also demonstrate that our method can provide practical advantages over the flag-state squasher when applied to discrete-variable protocols.

A numerical approach for the calculation of QKD key rates allows a uniform framework to be applied to general QKD protocols. Based on our group's previous work, we would like to build a universal software platform that is fully modularized and user-friendly, where one can easily swap in and out different QKD protocol descriptions, channel simulation models or experimental data, backend numerical solvers, and parameter optimization algorithms. Our goal is to build an open-source platform that can be both useful for theorists testing new protocols as well as experimentalists looking for optimal parameters or analyzing their experimental data.

In this work, we provide a complete, unconditional, asymptotic security analysis of DMCVQKD with four or more states. We do not need the photon-number cut-off assumption required in previous proofs. We derive inequalities that relate the result of a suitably chosen finite-dimensional optimization to the key rate. We solve the optimization numerically and utilize uniform continuity bounds to derive tight key rate lower bounds. We find that the key rates are comparable to previous conditional security proofs with the cut-off assumption, and to those achieved by Gaussian-modulated CVQKD.

Discrete-modulated continuous-variable quantum key distribution protocols are favorable due to the experimental simplicity and inherited properties of continuous-variable protocols. We provide a tight numerical key rate analysis of discrete-modulated continuous-variable quantum key distribution protocols in the asymptotic limit against collective attacks. As a specific example, we analyze the key rate of the quadrature phase-shift keying (QPSK) scheme in both the paranoid and realistic scenarios. When the detector noises are trusted, the QPSK scheme is expected to reach around 100 km with currently feasible experimental parameters. For both scenarios, we also investigate the performance of post-selection of data for the reverse reconciliation scheme and show that post-selection can provide improvements in the key rate as well as reducing the amount of data for post-processing.

Discrete-modulated continuous-variable quantum key distribution protocols are promising candidates for large-scale deployment due to the large technological overlap with deployed modern optical communication devices. The security of discrete modulation schemes has previously analyzed in the ideal detector scenario in the asymptotic limit. In this work, we calculate asymptotic key rates against collective attacks in the trusted detector noise scenario. Our results show that we can thus cut out most of the effect of detector noise and obtain asymptotic key rates similar to those had we access to ideal detectors.

Quantum key distribution (QKD) promises provably secure cryptography, even to attacks from an all-powerful adversary. However, with quantum computing development lagging behind QKD, the assumption that there exists an adversary equipped with a universal fault-tolerant quantum computer is unrealistic for at least the near future. Here, we explore the effect of restricting the eavesdropper's computational capabilities on the security of QKD, and find that improved secret key rates are possible. Specifically, we show that for a large class of discrete variable protocols higher key rates are possible if the eavesdropper is restricted to a unitary operation from the Clifford group. Further, we consider Clifford-random channels consisting of mixtures of Clifford gates. We numerically calculate a secret key rate lower bound for BB84 with this restriction, and show that in contrast to the case of a single restricted unitary attack, the mixture of Clifford based unitary attacks does not result in an improved key rate.

Finite key analysis of quantum key distribution (QKD) is an important tool for any QKD implementation. While much work has been done on the framework of finite key analysis, the application to individual protocols often relies on the the specific protocol being simple or highly symmetric as well as represented in small finite-dimensional Hilbert spaces. In this work, we extend our pre-existing reliable, efficient, tight, and generic numerical method for calculating the asymptotic key rate of device-dependent QKD protocols in finite-dimensional Hilbert spaces to the finite key regime using the security analysis framework of Renner. We explain how this extension preserves the reliability, efficiency, and tightness of the asymptotic method. We then explore examples which illustrate both the generality of our method as well as the importance of parameter estimation and data processing within the framework.

我们提出一个方案,在星型耦合腔QED网络中一步实现任意两个非直接耦合光腔中原子的两比特量子相位门操作。该操作是通过虚光子交换技术,使两个非直接耦合光腔中的原子与星型网络中心光腔中的辅助原子形成有效的非对称海森堡XY模型。通过数值模拟验证了方案的可行性。在系统的整个演化过程中腔模始终处于真空态,并且原子不被激发,原子的自发辐射与腔的衰减得到有效抑制,通过数值求解主方程可以证明操作对耗散不敏感。

Continuous-variable quantum key distribution (CV QKD) protocols with discrete modulation are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks, but their security analysis is less advanced than that of Gaussian modulation schemes. In this work, we apply a numerical method to analyze the security of discretemodulation protocols against collective attacks in the asymptotic limit, paving the way for a full security proof with finite-size effects. While our method is general for discrete-modulation schemes, we focus on two variants of the CV QKD protocol with quaternary modulation. Interestingly, thanks to the tightness of our proof method, we show that this protocol is capable of achieving much higher key rates over significantly longer distances with experimentally feasible parameters compared with previous security proofs of binary and ternary modulation schemes and also yielding key rates comparable to Gaussian modulation schemes. Furthermore, as our security analysis method is versatile, it allows us to evaluate variations of the discrete-modulated protocols, including direct and reverse reconciliation, and postselection strategies. In particular, we demonstrate that postselection of data in combination with reverse reconciliation can improve the key rates.

In this study, we propose a theoretical scheme for generating and stabilizing a maximally entangled state of two atoms trapped in two directly coupled cavities. Herein, two-level atoms arc coupled to the two quantized cavity fields with large detuning and that each atom is subjected to non-resonant driving by two weak classical fields. By introducing nonlocal bosonic modes, we find that the two identical atoms arc resonantly coupled to one of the collective optical cavity modes, whereas they arc coupled to the other collective optical cavity mode with large detuning. The target steady state can be prepared using the combined effect between the unitary dynamics of the classical fields and the dissipative process of the collective optical cavity modes in the dressed-state subspaces. The steady state can be prepared without requiring any special initial state. The numerical simulation shows that the Hell state can be obtained with high fidelity and that our scheme is robust to fluctuations of the system parameters.

Variations of phase-matching measurement-device-independent quantum key distribution (PM-MDI QKD) protocols have been investigated before, but it was recently discovered that this type of protocol (under the name of twin-field QKD) can beat the linear scaling of the repeaterless bound on secret key capacity. We propose a variation of PM-MDI QKD protocol, which reduces the sifting cost and uses non-phase-randomized coherent states as test states. We provide a security proof in the infinite key limit. Our proof is conceptually simple and gives tight key rates. We obtain an analytical key rate formula for the loss-only scenario, confirming the square root scaling and also showing the loss limit. We simulate the key rate for realistic imperfections and show that PM-MDI QKD can overcome the repeaterless bound with currently available technology.