Device-independent Quantum Key Distribution Protocols Research Articles

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.

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.

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.

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.

Improved DIQKD protocols with finite-size analysis

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.

Upper bound on device-independent quantum key distribution with two way classical postprocessing under individual attack

Device-independent quantum key distribution (DI-QKD) can guarantee the security even with untrusted devices. Unfortunately, conventional DI-QKD protocols can tolerate low noises only and require high detection efficiencies to achieve positive key rates. To improve the noise robustness, one promising solution is implementing the two-way classical postprocessing, which has the advantage of reducing the bit errors. In this paper, we study the DI-QKD with B-step two-way classical postprocessing under individual attacks. We adopt the tool of convex combination attack, i.e. an optimal individual attack, to upper bound the Devetak-Winter key rate. We show that, by using the B-step procedure, our protocol can tolerate detection efficiencies as low as and depolarising noise of 0.799, which is better than the thresholds for the protocol with one-way error correction. This result can serve as the lower bounds on the critical noise and detection efficiency for the scenarios under general attacks. Our work justifies the advantage of two-way classical postprocessing for DI-QKD, thus offering a step towards its applications.

Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints

According to the entropy accumulation theorem, proving the unconditional security of a device-independent quantum key distribution protocol reduces to deriving tradeoff functions, i.e., bounds on the single-round von Neumann entropy of the raw key as a function of Bell linear functionals, conditioned on an eavesdropper's quantum side information. In this work, we describe how the conditional entropy can be bounded in the 2-input/2-output setting, where the analysis can be reduced to qubit systems, by combining entropy bounds for variants of the well-known BB84 protocol with quantum constraints on qubit operators on the bipartite system shared by Alice and Bob. The approach gives analytic bounds on the entropy, or semi-analytic ones in reasonable computation time, which are typically close to optimal. We illustrate the approach on a variant of the device-independent CHSH QKD protocol where both bases are used to generate the key as well as on a more refined analysis of the original single-basis variant with respect to losses. We obtain in particular a detection efficiency threshold slightly below 80.26%, within reach of current experimental capabilities.

A device-independent quantum key distribution system for distant users

Device-independent quantum key distribution (DIQKD) enables the generation of secret keys over an untrusted channel using uncharacterized and potentially untrusted devices1–9. The proper and secure functioning of the devices can be certified by a statistical test using a Bell inequality10–12. This test originates from the foundations of quantum physics and also ensures robustness against implementation loopholes13, thereby leaving only the integrity of the users’ locations to be guaranteed by other means. The realization of DIQKD, however, is extremely challenging—mainly because it is difficult to establish high-quality entangled states between two remote locations with high detection efficiency. Here we present an experimental system that enables for DIQKD between two distant users. The experiment is based on the generation and analysis of event-ready entanglement between two independently trapped single rubidium atoms located in buildings 400 metre apart14. By achieving an entanglement fidelity of {mathcal F} ,ge 0.892(23) and implementing a DIQKD protocol with random key basis15, we observe a significant violation of a Bell inequality of S = 2.578(75)—above the classical limit of 2—and a quantum bit error rate of only 0.078(9). For the protocol, this results in a secret key rate of 0.07 bits per entanglement generation event in the asymptotic limit, and thus demonstrates the system’s capability to generate secret keys. Our results of secure key exchange with potentially untrusted devices pave the way to the ultimate form of quantum secure communications in future quantum networks.

Device-independent secret key rates via a postselected Bell inequality

In device-independent quantum key distribution (DIQKD) the security is not based on any assumptions about the intrinsic properties of the devices and the quantum signals but on the violation of a Bell inequality. We introduce a DIQKD scenario in which an optimal Bell inequality is constructed from the performed measurement data rather than fixing beforehand a specific Bell inequality. Our method can be employed in a general way, for any number of measurement settings and any number of outcomes. We provide an implementable DIQKD protocol and perform finite-size security key analysis for collective attacks. We compare our approach with related procedures in the literature and analyze the robustness of our protocol. We also study the performance of our method in several Bell scenarios as well as for random measurement settings.

Device-independent quantum key distribution from computational assumptions

In device-independent quantum key distribution (DIQKD), an adversary prepares a device consisting of two components, distributed to Alice and Bob, who use the device to generate a secure key. The security of existing DIQKD schemes holds under the assumption that the two components of the device cannot communicate with one another during the protocol execution. This is called the no-communication assumption in DIQKD. Here, we show how to replace this assumption, which can be hard to enforce in practice, by a standard computational assumption from post-quantum cryptography: we give a protocol that produces secure keys even when the components of an adversarial device can exchange arbitrary quantum communication, assuming the device is computationally bounded. Importantly, the computational assumption only needs to hold during the protocol execution—the keys generated at the end of the protocol are information-theoretically secure as in standard DIQKD protocols.

Computing secure key rates for quantum cryptography with untrusted devices

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 semidefinite 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.

Bell Nonlocality Is Not Sufficient for the Security of Standard Device-Independent Quantum Key Distribution Protocols.

Device-independent quantum key distribution is a secure quantum cryptographic paradigm that allows two honest users to establish a secret key, while putting minimal trust in their devices. Most of the existing protocols have the following structure: first, a bipartite nonlocal quantum state is distributed between the honest users, who perform local projective measurements to establish nonlocal correlations. Then, they announce the implemented measurements and extract a secure key by postprocessing their measurement outcomes. We show that no protocol of this form allows for establishing a secret key when implemented on any correlation obtained by measuring local projective measurements on certain entangled nonlocal states, namely, on a range of entangled two-qubit Werner states. To prove this result, we introduce a technique for upper bounding the asymptotic key rate of device-independent quantum key distribution protocols, based on a simple eavesdropping attack. Our results imply that either different reconciliation techniques are needed for device-independent quantum key distribution in the large-noise regime, or Bell nonlocality is not sufficient for this task.

Device-independent quantum key distribution based on Bell inequalities with more than two inputs and two outputs

Device-independent quantum key distribution (DI-QKD) offers the strongest form of security against eavesdroppers bounded by the laws of quantum mechanics. However, a practical implementation is still pending due to the requirement of combinations of visibility and detection efficiency that are beyond those possible with current technology. This mismatch motivates the search for DI-QKD protocols that can close the gap between theoretical and practical security. In this work, we present two DI-QKD protocols whose security relies on Bell inequalities with more than two inputs and two outputs. We show that, for maximally entangled states and perfect visibility, a protocol based on a Bell inequality with three inputs and four outputs requires a slightly lower detection efficiency than the protocols based on Bell inequalities with two inputs and two outputs.

Device-independent quantum key distribution with random key basis

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 108–1010 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.

Device-independent quantum key distribution with asymmetric CHSH inequalities

The simplest device-independent quantum key distribution protocol is based on the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality and allows two users, Alice and Bob, to generate a secret key if they observe sufficiently strong correlations. There is, however, a mismatch between the protocol, in which only one of Alice's measurements is used to generate the key, and the CHSH expression, which is symmetric with respect to Alice's two measurements. We therefore investigate the impact of using an extended family of Bell expressions where we give different weights to Alice's measurements. Using this family of asymmetric Bell expressions improves the robustness of the key distribution protocol for certain experimentally-relevant correlations. As an example, the tolerable error rate improves from 7.15% to about 7.42% for the depolarising channel. Adding random noise to Alice's key before the postprocessing pushes the threshold further to more than 8.34%. The main technical result of our work is a tight bound on the von Neumann entropy of one of Alice's measurement outcomes conditioned on a quantum eavesdropper for the family of asymmetric CHSH expressions we consider and allowing for an arbitrary amount of noise preprocessing.

Overcoming the rate-distance limit of device-independent quantum key distribution.

Device-independent quantum key distribution (DIQKD) exploits the violation of a Bell inequality to extract secure keys even if users' devices are untrusted. Currently, all DIQKD protocols suffer from the secret key capacity bound, i.e., the secret key rate scales linearly with the transmittance of two users. Here we propose a heralded DIQKD scheme based on entangled coherent states to improve entangling rates whereby long-distance entanglement is created by single-photon-type interference. The secret key rate of our scheme can significantly outperform the traditional two-photon-type Bell-state measurement scheme and, importantly, surpass the above capacity bound. Our protocol therefore is an important step towards a realization of DIQKD and can be a promising candidate scheme for entanglement swapping in the future quantum internet.

Device-independent quantum key distribution with single-photon sources

Device-independent quantum key distribution protocols allow two honest users to establish a secret key with minimal levels of trust on the provider, as security is proven without any assumption on the inner working of the devices used for the distribution. Unfortunately, the implementation of these protocols is challenging, as it requires the observation of a large Bell-inequality violation between the two distant users. Here, we introduce novel photonic protocols for device-independent quantum key distribution exploiting single-photon sources and heralding-type architectures. The heralding process is designed so that transmission losses become irrelevant for security. We then show how the use of single-photon sources for entanglement distribution in these architectures, instead of standard entangled-pair generation schemes, provides significant improvements on the attainable key rates and distances over previous proposals. Given the current progress in single-photon sources, our work opens up a promising avenue for device-independent quantum key distribution implementations.

Completely device-independent quantum key distribution

Quantum key distribution (QKD) is a provably secure way for two distant parties to establish a common secret key, which then can be used in a classical cryptographic scheme. Using quantum entanglement, one can reduce the necessary assumptions that the parties have to make about their devices, giving rise to device-independent QKD (DIQKD). However, in all existing protocols to date the parties need to have an initial (at least partially) random seed as a resource. In this work, we show that this requirement can be dropped. Using recent advances in the fields of randomness amplification and randomness expansion, we demonstrate that it is sufficient for the message the parties want to communicate to be (partially) unknown to the adversaries -- an assumption without which any type of cryptography would be pointless to begin with. One party can use her secret message to locally generate a secret sequence of bits, which can then be openly used by herself and the other party in a DIQKD protocol. Hence, our work reduces the requirements needed to perform secure DIQKD and establish safe communication.

Loss tolerant device-independent quantum key distribution: a proof of principle

We here present the rate analysis and a proof of principle demonstration of a device-independent quantum key distribution protocol requiring the lowest detection efficiency necessary to achieve a secure key compared to device-independent protocols known so far. The protocol is based on a non-maximally entangled state and its experimental demonstration has been performed by two-photon bipartite entangled states. The improvement with respect to protocols involving maximally entangled states has been estimated.