Device-independent Quantum Cryptography Research Articles

Full network nonlocality sharing in extended bilocal scenario via weak measurements with the optimal pointer

The investigation of network nonlocality (NN) has expanded the study of quantum nonlocality, yet it fails to fully capture the complexities within quantum networks. Recently, a stronger and more genuine definition of NN, known as full quantum network nonlocality (FNN), has been explored, which is considered a vital resource for realizing network-based device-independent quantum cryptography protocols. In this work, we explore the recycling of FNN as quantum resources by analyzing the FNN sharing between different combinations of observers. The FNN sharing in an extended bilocal scenario (consisting of two independent two-qubit quantum states as sources) via weak measurements has been thoroughly discussed. Based on the different motivations of the observer-Charlie1, two types of possible FNN sharing, passive FNN sharing and active FNN sharing, can be investigated by checking the simultaneous violation of Kerstjens–Gisin–Tavakoli inequalities between Alice-Bob-Charlie1 and Alice-Bob-Charlie2. Our results show that passive FNN sharing is impossible while active FNN sharing can be achieved through proper measurements, indicating that FNN sharing in this scenario requires more cooperation by intermediate observers compared to Bell nonlocality sharing and NN sharing.

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.

Optimal tests of genuine multipartite nonlocality

We propose an optimal and efficient numerical test for witnessing genuine multipartite nonlocality based on a geometric approach. In particular, we consider two non-equivalent models of local hidden variables, namely the Svetlichny and the no-signaling bilocal models. While our knowledge concerning these models is well established for Bell-type scenarios involving two measurement settings per party, the general case based on an arbitrary number of settings is a considerably more challenging task and very little work has been done in this field. In this paper, we applied such general tests to detect and characterize genuine n-way nonlocal correlations for various states of three qubits and qutrits. Apart from the fundamental problem of characterizing genuine multipartite nonlocal correlations, the extension of the number of measurements beyond two is also of practical importance. As a measure of nonlocality, we use the probability of violation of local realism under randomly sampled observables, and the strength of nonlocality, described by the resistance to white noise admixture. In particular, we analyze to what extent the Bell-type scenario involving two measurement settings can be used to certify genuine n-way nonlocal correlations generated for more general models. In addition, we propose a simple procedure to detect such nonlocal correlations for randomly chosen settings with an efficiency of up to 100%. Due to its near-perfect efficiency, our method may open new possibilities in device-independent quantum cryptography applications where strong nonlocality between all partners is required.

Optimal strategy to certify quantum nonlocality

Certification of quantum nonlocality plays a central role in practical applications like device-independent quantum cryptography and random number generation protocols. These applications entail the challenging problem of certifying quantum nonlocality, something that is hard to achieve when the target quantum state is only weakly entangled, or when the source of errors is high, e.g. when photons propagate through the atmosphere or a long optical fiber. Here we introduce a technique to find a Bell inequality with the largest possible gap between the quantum prediction and the classical local hidden variable limit for a given set of measurement frequencies. Our method represents an efficient strategy to certify quantum nonlocal correlations from experimental data without requiring extra measurements, in the sense that there is no Bell inequality with a larger gap than the one provided. Furthermore, we also reduce the photodetector efficiency required to close the detection loophole. We illustrate our technique by improving the detection of quantum nonlocality from experimental data obtained with weakly entangled photons.

Collective multipartite Einstein-Podolsky-Rosen steering via cascaded four-wave mixing of rubidium atoms

Collective multipartite Einstein-Podolsky-Rosen (EPR) steering is a type of quantum correlation shared among $n$ parties, where the EPR paradox of one party can be realized only by performing local measurements on all the remaining $n\ensuremath{-}1$ parties. Here, we propose an efficient method to produce collective multipartite EPR steering via symmetrically and asymmetrically cascading parametric amplification processes, i.e., four-wave mixing (FWM) of rubidium atoms. The simplified collective-steering criterion is introduced using the Coffman-Kundu-Wootters monogamy relation. Moreover, by actively adjusting the parametric gains, the collective EPR steerability is optimized in our schemes. We find that the scale of collective steering can be extended by cascading more FWMs; in particular, introducing optical loss is useful for generating collective steering with more parties only in the asymmetry structure. Our results pave the way for the construction of quantum networks and provide a promising candidate for one-sided device-independent quantum cryptography among multiple users.

Einstein-Podolsky-Rosen entanglement and asymmetric steering between distant macroscopic mechanical and magnonic systems

We propose a deterministic scheme for establishing hybrid Einstein-Podolsky-Rosen (EPR) entanglement channel between a macroscopic mechanical oscillator and a magnon mode in a distant yttrium-iron-garnet (YIG) sphere across about ten gigahertz of frequency difference. The system consists of a driven electromechanical cavity which is unidirectionally coupled to a distant electromagnonical cavity inside which a YIG sphere is placed. We find that far beyond the sideband-resolved regime in the electromechanical subsystem, stationary phonon-magnon EPR entanglement can be achieved. This is realized by utilizing the output field of the electromechanical cavity being an intermediary which distributes the electromechanical entanglement to the magnons, thus establishing a remote phonon-magnon entanglement. The EPR entanglement is strong enough such that phonon-magnon quantum steering can be attainable in an asymmetric manner. This long-distance macroscopic hybrid EPR entanglement and steering enable potential applications not only in fundamental tests of quantum mechanics at the macro scale, but also in quantum networking and one-sided device-independent quantum cryptography based on magnonics and electromechanics.

Graphical Methods in Device-Independent Quantum Cryptography

We introduce a framework for graphical security proofs in device-independent quantum cryptography using the methods of categorical quantum mechanics. We are optimistic that this approach will make some of the highly complex proofs in quantum cryptography more accessible, facilitate the discovery of new proofs, and enable automated proof verification. As an example of our framework, we reprove a previous result from device-independent quantum cryptography: any linear randomness expansion protocol can be converted into an unbounded randomness expansion protocol. We give a graphical proof of this result, and implement part of it in the Globular proof assistant.

The power of independence

Device-independent quantum cryptography promises unprecedented security, but it is regarded as a theorist's dream and an experimentalist's nightmare. A new mathematical tool has now pushed its experimental demonstration much closer to reality.

Randomness in nonlocal games between mistrustful players

If two quantum players at a nonlocal game G achieve a superclassical score, then their measurement outcomes must be at least partially random from the perspective of any third player. This is the basis for device-independent quantum cryptography. In this paper we address a related question: does a superclassical score at G guarantee that one player has created randomness from the perspective of the other player? We show that for complete-support games, the answer is yes: even if the second player is given the first player’s input at the conclusion of the game, he cannot perfectly recover her output. Thus some amount of local randomness (i.e., randomness possessed by only one player) is always obtained when randomness is certified from nonlocal games with quantum strategies. This is in contrast to non-signaling game strategies, which may produce global randomness without any local randomness. We discuss potential implications for cryptographic protocols between mistrustful parties.

Einstein-Podolsky-Rosen steering and quantum steering ellipsoids: Optimal two-qubit states and projective measurements

We identify the families of states that maximise some recently proposed quantifiers of Einstein-Podolsky-Rosen (EPR) steering and the volume of the Quantum Steering Ellipsoid (QSE). The optimal measurements which maximise genuine EPR steering measures are discussed and we develop a novel way to find them using the QSE. We thus explore the links between genuine EPR steering and the QSE and introduce states that can be the most useful for one-sided device-independent quantum cryptography for a given amount of noise.

Quantum discord as a resource for quantum cryptography.

Quantum discord is the minimal bipartite resource which is needed for a secure quantum key distribution, being a cryptographic primitive equivalent to non-orthogonality. Its role becomes crucial in device-dependent quantum cryptography, where the presence of preparation and detection noise (inaccessible to all parties) may be so strong to prevent the distribution and distillation of entanglement. The necessity of entanglement is re-affirmed in the stronger scenario of device-independent quantum cryptography, where all sources of noise are ascribed to the eavesdropper.

Device-independent quantum cryptography for continuous variables

We present the first device-independent quantum cryptography protocol for continuous variables. Our scheme is based on the Gottesman-Kitaev-Preskill encoding scheme whereby a qubit is embedded in the infinite-dimensional space of a quantum harmonic oscillator. The novel application of discrete-variable device-independent quantum key distribution to this encoding enables a continuous-variable analogue. Since the security of this protocol is based on discrete-variables we inherit by default security against collective attacks and, under certain memoryless assumptions, coherent attacks. We find that our protocol is valid over the same distances as its discrete-variable counterpart, except that we are able to take advantage of high efficiency commercially available detectors where, for the most part, only homodyne detection is required. This offers the potential of removing the difficulty in closing the loopholes associated with Bell inequalities.

Victory for the Quantum Code Maker?

To fend off potential hackers, researchers have taken a theoretical step closer to realizing a device-independent quantum cryptography protocol.

Entropic uncertainty from effective anticommutators

We investigate entropic uncertainty relations for two or more binary measurements, for example, spin-$\frac{1}{2}$ or polarization measurements. We argue that the effective anticommutators of these measurements, i.e., the anticommutators evaluated on the state prior to measuring, are an expedient measure of measurement incompatibility. Based on the knowledge of pairwise effective anticommutators we derive a class of entropic uncertainty relations in terms of conditional R\'enyi entropies. Our uncertainty relations are formulated in terms of effective measures of incompatibility, which can be certified in a device-independent fashion. Consequently, we discuss potential applications of our findings to device-independent quantum cryptography. Moreover, to investigate the tightness of our analysis we consider the simplest (and very well studied) scenario of two measurements on a qubit. We find that our results outperform the celebrated bound due to Maassen and Uffink [Phys. Rev. Lett. 60, 1103 (1988)] and provide an analytical expression for the minimum uncertainty which also outperforms some recent bounds based on majorization.

Characterization of Quantum Correlations with Local Dimension Constraints and Its Device-Independent Applications

Device-independent quantum cryptography protocols exploit quantum correlations generated by ``black box'' quantum devices. The physical dimensionality of such devices may act as a constraint. But which quantum correlations are fundamentally attainable and can be exploited under this constraint? Scientists now develop a new and timely numerical method that answers this question.

A monogamy-of-entanglement game with applications to device-independent quantum cryptography

We consider a game in which two separate laboratories collaborate to prepare a quantum system and are then asked to guess the outcome of a measurement performed by a third party in a random basis on that system. Intuitively, by the uncertainty principle and the monogamy of entanglement, the probability that both players simultaneously succeed in guessing the outcome correctly is bounded. We are interested in the question of how the success probability scales when many such games are performed in parallel. We show that any strategy that maximizes the probability to win every game individually is also optimal for the parallel repetition of the game. Our result implies that the optimal guessing probability can be achieved without the use of entanglement. We explore several applications of this result. Firstly, we show that it implies security for standard BB84 quantum key distribution when the receiving party uses fully untrusted measurement devices, i.e. we show that BB84 is one-sided device independent. Secondly, we show how our result can be used to prove security of a one-round position-verification scheme. Finally, we generalize a well-known uncertainty relation for the guessing probability to quantum side information.

Memory Attacks on Device-Independent Quantum Cryptography

Device-independent quantum cryptographic schemes aim to guarantee security to users based only on the output statistics of any components used, and without the need to verify their internal functionality. Since this would protect users against untrustworthy or incompetent manufacturers, sabotage, or device degradation, this idea has excited much interest, and many device-independent schemes have been proposed. Here we identify a critical weakness of device-independent protocols that rely on public communication between secure laboratories. Untrusted devices may record their inputs and outputs and reveal information about them via publicly discussed outputs during later runs. Reusing devices thus compromises the security of a protocol and risks leaking secret data. Possible defenses include securely destroying or isolating used devices. However, these are costly and often impractical. We propose other more practical partial defenses as well as a new protocol structure for device-independent quantum key distribution that aims to achieve composable security in the case of two parties using a small number of devices to repeatedly share keys with each other (and no other party).