Device-independent Quantum Key Distribution Research Articles

Device-independent quantum key distribution with realistic single-photon source implementations

Device-independent quantum key distribution (DIQKD) aims at generating secret keys between distant parties without the parties trusting their devices. We investigate a proposal for performing fully photonic DIQKD, based on single photon sources and heralding measurements at a central station placed between the two parties. We derive conditions to attain non-zero secret-key rates in terms of the photon efficiency, indistinguishability and the second order autocorrelation function of the single-photon sources. Exploiting new results on the security bound of such protocols allows us to reduce the requirements on the physical parameters of the setup. Our analysis shows that in the considered schemes, key rates of several hundreds of secret bits per second are within reach at distances of several tens of kilometers.

Quantum key distribution using deterministic single-photon sources over a field-installed fibre link

Quantum-dot-based single-photon sources are key assets for quantum information technology, supplying on-demand scalable quantum resources for computing and communication. However, long-lasting issues such as limited long-term stability and source brightness have traditionally impeded their adoption in real-world applications. Here, we realize a quantum key distribution field trial using true single photons across an 18-km-long dark fibre, located in the Copenhagen metropolitan area, using an optimized, state-of-the-art, quantum-dot single-photon source frequency-converted to the telecom wavelength. A secret key generation rate of > 2 kbits/s realized over a 9.6 dB channel loss is achieved with a polarization-encoded BB84 scheme, showing remarkable stability for more than 24 hours of continuous operation. Our results highlight the maturity of deterministic single-photon source technology while paving the way for advanced single-photon-based communication protocols, including fully device-independent quantum key distribution, towards the goal of a quantum internet.

Upper bounds on key rates in device-independent quantum key distribution based on convex-combination attacks

Upper bounds on key rates in device-independent quantum key distribution based on convex-combination attacks

Monte Carlo approach to the evaluation of the security of device-independent quantum key distribution

We present a generic study on the information-theoretic security of multi-setting device-independent quantum key distribution (DIQKD) protocols, i.e. ones that involve more than two measurements (or inputs) for each party to perform, and yield dichotomic results (or outputs). The approach we develop, when applied in protocols with either symmetric or asymmetric Bell experiments, yields nontrivial upper bounds on the secure key rates, along with the detection efficiencies required upon the measuring devices. The results imply that increasing the number of measurements may lower the detection efficiency required by the security criterion. The improvement, however, depends on (i) the choice of multi-setting Bell inequalities chosen to be tested in a protocol, and (ii) either a symmetric or asymmetric Bell experiment is considered. Our results serve as an advance toward the quest for evaluating security and reducing efficiency requirement of applying DIQKD in scenarios without heralding.

Manipulating the direction of one-way steering in an optomechanical ring cavity

Quantum steering refers to the apparent possibility of exploiting nonseparable quantum correlations to remotely influence the quantum state of an observer via local measurements. Different from entanglement and Bell nonlocality, quantum steering exhibits an inherent asymmetric property, which makes it relevant for many asymmetric quantum information processing tasks. Here, we study Gaussian quantum steering between two mechanical modes in an optomechanical ring cavity. Using experimentally feasible parameters, we show that the state of the two considered modes can exhibit two-way steering and even one-way steering. Instead of using unbalanced losses or noises, we propose a simple practical way to control the direction of one-way steering. A comparative study between the steering and entanglement of the studied modes shows that both steering and entanglement undergo a sudden death-like behavior. In particular, steering is found more fragile against thermal noise remaining constantly upper-bounded by entanglement. The proposed scheme may be meaningful for one-sided device-independent quantum key distribution, where the security of such protocol depends fundamentally on the direction of steering.

Single-Qubit Loss-Tolerant Quantum Position Verification Protocol Secure against Entangled Attackers.

We give a tight characterization of the relation between loss tolerance and error rate of the most popular protocol for quantum position verification, which is based on BB84 states. Combining it with classical information, we show, using semidefinite programming, for the first time a fault-tolerant protocol that is secure against attackers who preshare a linear amount of entanglement (in the classical information), arbitrarily slow quantum information and that tolerates a certain amount of photon loss. We also extend this analysis to the case of more than two bases, showing even stronger loss tolerance for that case. Finally, we show that our techniques can be applied to improve the analysis of one-sided device-independent quantum key distribution protocols.

Impact of imperfect measurements on multi-party quantum key distribution

The imperfection of measurements in real-world scenarios can compromise the performance of device-independent quantum key distribution (DIQKD) protocols. In this paper, we focus on a specific DIQKD protocol that relies on the violation of the Svetlichny’s inequality (SI), considering an eavesdropper utilizing the convex combination attack. Our analysis covers both the three-party DIQKD case and the general n-party scenario. Our main result is the relationship between the measurement accuracy and the extractable secret-key rate in all multi-party scenarios. The result demonstrates that as measurement accuracy improves, the extractable secret-key rate approaches 1, reaching its maximum value when the measurement accuracy is perfect. We reveal that achieving positive extractable secret-key rates requires a threshold measurement accuracy that is consistently higher than the critical measurement accuracy necessary to violate the SI. We depict these thresholds for n-party scenarios ranging from n=3 to n=10, demonstrating that as the number of parties (n) increases, both thresholds exhibit a rapid and monotonic convergence towards unity. Furthermore, we consider a scenario involving a non-maximally entangled state with imperfect measurements, where the emission of the initial GHZ state undergoes noise during transmission, resulting in a Werner state. The study further quantifies and demonstrates the relationship between the extractable secret-key rate, the visibility of the Werner state, and the measurement accuracy, specifically emphasizing the three-party scenario. This study aims to illuminate the influence of imperfect measurement accuracy on the security and performance of multi-party DIQKD protocols. The results emphasize the importance of high measurement accuracy in achieving positive secret-key rates and maintaining the violation of the SI.

Quantum Complementarity Approach to Device-Independent Security.

Complementarity is an essential feature of quantum mechanics. The preparation of an eigenstate of one observable implies complete randomness in its complementary observable. In quantum cryptography, complementarity allows us to formulate security analyses in terms of phase-error correction. However, the concept becomes much subtler in the device-independent regime that offers security without device characterization. Security proofs of device-independent quantum cryptography tasks are often complex and quite different from those of their more standard device-dependent cousins. The existing proofs pose huge challenges to experiments, among which large data-size requirement is a crux. Here, we show the complementarity security origin of the device-independent tasks. By linking complementarity with quantum nonlocality, we recast the device-independent scheme into a quantum error correction protocol. Going beyond the identical-and-independent-distribution case, we consider the most general attack. We generalize the sample entropy in classical Shannon theory for the finite-size analysis. Our method exhibits good finite-size performance and brings the device-independent scheme to a more practical regime. Applying it to the data in a recent ion-trap-based device-independent quantum key distribution experiment, one could reduce the requirement on data size to less than a third. Furthermore, the operational meaning of complementarity naturally extends device-independent scenarios to advantage key distillation, easing experiments by tolerating higher loss and lower transmittance.

Measurement device-independent quantum key distribution with vector vortex modes under diverse weather conditions

Most quantum key distribution schemes exploiting orbital angular momentum-carrying optical beams are based on conventional set-ups, opening up the possibility of detector side-channel attacks. These optical beams also suffer from spatial aberrations due to atmospheric turbulence and unfavorable weather conditions. Consequently, we introduce a measurement device-independent quantum key distribution implemented with vector vortex modes. We study the transmission of vector vortex and scalar beams through a turbulent atmospheric link under diverse weather conditions such as rain or haze. We demonstrate that a maximum secure key transmission distance of 178 km can be achieved under clear conditions by utilizing the vector vortex beams, which have been mainly ignored in the literature. When raindrops have a diameter of 6 mm and fog particles have a radius of 0.5 upmum, the signals can reach 152 km and 160 km, respectively. Since these distances are comparable, this work sheds light into the feasibility of implementing measurement device-independent quantum key distribution using vector vortex modes under diverse weather conditions. Most significantly, this opens the door to practical secure quantum communications.

De Finetti Theorems for Quantum Conditional Probability Distributions with Symmetry

The aim of device-independent quantum key distribution (DIQKD) is to study protocols that allow the generation of a secret shared key between two parties under minimal assumptions on the devices that produce the key. These devices are merely modeled as black boxes and mathematically described as conditional probability distributions. A major obstacle in the analysis of DIQKD protocols is the huge space of possible black box behaviors. De Finetti theorems can help to overcome this problem by reducing the analysis to black boxes that have an iid structure. Here we show two new de Finetti theorems that relate conditional probability distributions in the quantum set to de Finetti distributions (convex combinations of iid distributions) that are themselves in the quantum set. We also show how one of these de Finetti theorems can be used to enforce some restrictions onto the attacker of a DIQKD protocol. Finally we observe that some desirable strengthenings of this restriction, for instance to collective attacks only, are not straightforwardly possible.

Device-Independent Quantum Key Distribution Based on the Mermin-Peres Magic Square Game.

Device-independent quantum key distribution (DIQKD) is information-theoretically secure against adversaries who possess a scalable quantum computer and who have supplied malicious key-establishment systems; however, the DIQKD key rate is currently too low. Consequently, we devise a DIQKD scheme based on the quantum nonlocal Mermin-Peres magic square game: our scheme asymptotically delivers DIQKD against collective attacks, even with noise. Our scheme outperforms DIQKD using the Clauser-Horne-Shimony-Holt game with respect to the number of game rounds, albeit not number of entangled pairs, provided that both state visibility and detection efficiency are high enough.

Composably secure device-independent encryption with certified deletion

We study the task of encryption with certified deletion (ECD) introduced by Broadbent and Islam (2020), but in a device-independent setting: we show that it is possible to achieve this task even when the honest parties do not trust their quantum devices. Moreover, we define security for the ECD task in a composable manner and show that our ECD protocol satisfies conditions that lead to composable security. Our protocol is based on device-independent quantum key distribution (DIQKD), and in particular the parallel DIQKD protocol based on the magic square non-local game, given by Jain, Miller and Shi (2020). To achieve certified deletion, we use a property of the magic square game observed by Fu and Miller (2018), namely that a two-round variant of the game can be used to certify deletion of a single random bit. In order to achieve certified deletion security for arbitrarily long messages from this property, we prove a parallel repetition theorem for two-round non-local games, which may be of independent interest.

Dissipative generation of significant amount of photon-phonon asymmetric steering in magnomechanical interfaces

A theoretical scheme is proposed to generate significant amount of photon-phonon entanglement and asymmetric steering in a cavity magnomechanical system, which is constituted by trapping a yttrium iron garnet sphere in a microwave cavity. By applying a blue-detuned microwave driving field, we obtain an effective Hamiltonian where the magnon mode acting as an engineered resevoir cools the Bogoliubov modes of microwave cavity mode and mechanical mode via a beam-splitter-like interaction. By this means, the microwave cavity mode and mechanical mode can be driven to a two-mode squeezed state in the stationary limit. Particularly, strong two-way and one-way photon-phonon asymmetric quantum steering can be obtained with even equal dissipation. It is widely divergent with the conventional proposal, where additional unbalanced losses or noises should be imposed on the two subsystems. Our finding may be significant to expand our understanding of the essential physics of asymmetric steering and extend the potential application of the cavity spintronics to device-independent quantum key distribution.

Automated design of quantum-optical experiments for device-independent quantum key distribution

Automated design of quantum-optical experiments for device-independent quantum key distribution

Optimal Statistical Analyses of Bell Experiments

We show how both smaller and more reliable p-values can be computed in Bell-type experiments by using statistical deviations from no-signalling equalities to reduce statistical noise in the estimation of Bell’s S or Eberhard’s J. Further improvement was obtained by using the Wilks likelihood ratio test based on the four tetranomially distributed vectors of counts of the four different outcome combinations, one 4-vector for each of the four setting combinations. The methodology was illustrated by application to the loophole-free Bell experiments of 2015 and 2016 performed in Delft and Munich, at NIST, and in Vienna, respectively, and also to the earlier (1998) Innsbruck experiment of Weihs et al. and the recent (2022) Munich experiment of Zhang et al., which investigates the use of a loophole-free Bell experiment as part of a protocol for device-independent quantum key distribution (DIQKD).

Controlled Entanglement Source for Quantum Cryptography

Quantum entanglement has become an essential resource in quantum information processing. Existing works employ entangled quantum states to perform various tasks, while little attention is paid to the control of the resource. In this work, we propose a simple protocol to upgrade an entanglement source with access control through phase randomization at the optical pump. The enhanced source can effectively control all users in utilizing the entanglement resource to implement quantum cryptography. In addition, we show this control can act as a practical countermeasure against memory attack on device-independent quantum key distribution at a negligible cost. To demonstrate the feasibility of our protocol, we implement an experimental setup using just off-the-shelf components and characterize its performance accordingly.

Security of device-independent quantum key distribution protocols: a review

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.

Counterfactual quantum key distribution with untrusted detectors

Compared with the traditional BB84 protocol, the counterfactual quantum key distribution (QKD) does not rely on any signal travelling in the quantum channel, and therefore can present a security advantage where Eve cannot fully access signal. However, the practical system may be damaged in a scenario where the devices are untrusted. In this paper, we analyze the security of counterfactual QKD in untrusted detectors scenario. We show that the requirement to disclose “which detector clicked” has become the main loophole in all counterfactual QKD versions. An eavesdropping scheme which is similar to the memory attack on device-independent QKD could break its security by exploiting detectors' imperfections. We consider two different counterfactual QKD protocols and analyze their security against this major loophole. One is a modified Noh09 protocol, which would be secure in untrusted detectors context. Another is a variant of counterfactual QKD with high efficiency (Phys. Rev. A 104 (2021) 022424) against a series of detectors side-channel attacks as well as against other attacks that exploit detectors imperfections.

High-dimensional quantum key distribution implemented with biphotons

We present a high-dimensional measurement device-independent (MDI) quantum key distribution (QKD) protocol employing biphotons to encode information. We exploit the biphotons as qutrits to improve the tolerance to error rate. Qutrits have a larger quantum system; hence they carry more bits of classical information and have improved robustness against eavesdropping compared to qubits. Notably, our proposed protocol is independent of measurement devices, thus eliminating the possibility of side-channel attacks. Also, we employ the finite key analysis approach to study the performance of our proposed protocol under realistic conditions where finite resources are used. Furthermore, we simulated the secret key rate for the proposed protocol in terms of the transmission distance for different fixed amounts of signals. The results prove that this protocol achieves a considerable secret key rate for a moderate transmission distance of 90 km by using 10^{16} signals. Moreover, the expected secret key rate was simulated to examine our protocol’s performance at various intrinsic error rate values, Q=(0.3%,0.6%,1%) caused by misalignment and instability due to the optical system. These results show that reasonable key rates are achieved with a minimum data size of about 10^{14} signals which are realizable with the current technology. Thus, implementing MDI-QKD using finite resources while allowing intrinsic errors due to the optical system makes a giant step forward toward realizing practical QKD implementations.

Eavesdropping a quantum key distribution network using sequential quantum unsharp measurement attacks

We investigate the possibility of eavesdropping on a quantum key distribution network by local sequential quantum unsharp measurement attacks by the eavesdropper. In particular, we consider a pure two-qubit state shared between two parties Alice and Bob, sharing quantum steerable correlations that form the one-sided device-independent quantum key distribution network. One qubit of the shared state is with Alice and the other one while going to Bob’s place is intercepted by multiple sequential eavesdroppers who perform quantum unsharp measurement attacks thus gaining some positive key rate while preserving the quantum steerable correlations for Bob. In this way, Bob will also have a positive secret key rate although reduced. However, this reduction is not that sharp and can be perceived due to the decoherence and imperfection of the measurement devices. We found that there is a possibility of sequential eavesdropping even after setting a minimum threshold on the observed secure key rate by Alice and Bob. In the end, we show that an unbounded number of eavesdroppers can also get secret information in some specific scenario.