Device-independent Setting Research Articles

Investigating device-independent quantum random number generation

Quantum random number generation (QRNG) is a resource that is a necessity in the field of cryptography. However, its certification has been challenging. In this article, we certify randomness with the aid of quantum entanglement in a device independent setting, where we choose two-photon interference for source characterisation. The CHSH inequality violation and quantum state tomography are used as independent checks on the measurement devices. These measures ensure the unpredictability of quantum random number generation. This work can be easily extended to faster randomness expansion protocols.

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.

Self-Testing of any Pure Entangled State with the Minimal Number of Measurements and Optimal Randomness Certification in a One-Sided Device-Independent Scenario

Certification of quantum systems and their properties has become a field of intensive studies. Here, taking advantage of the one-sided device-independent scenario (known also as quantum steering scenario), we propose a self-testing scheme for all bipartite entangled states using a single family of steering inequalities with the minimal number of two measurements per party. Building on this scheme we then show how to certify all rank-one extremal measurements, including non-projective $d^2$-outcome measurements, which in turn can be used for certification of the maximal amount of randomness from every entangled bipartite state of local dimension $d$, that is, $2\log_2d$ bits. Finally, in a particular case of $d=3$, we extend our self-testing results to the fully device-independent setting.

Quick Quantum Steering: Overcoming Loss and Noise with Qudits

A primary requirement for a robust and unconditionally secure quantum network is the establishment of quantum nonlocal correlations over a realistic channel. While loophole-free tests of Bell nonlocality allow for entanglement certification in such a device-independent setting, they are extremely sensitive to loss and noise, which naturally arise in any practical communication scenario. Quantum steering relaxes the strict technological constraints of Bell nonlocality by reframing it in an asymmetric manner, with a trusted party only on one side. However, tests of quantum steering still require either extremely high-quality entanglement or very low loss. Here we introduce a test of quantum steering that harnesses the advantages of high-dimensional entanglement to be simultaneously noise robust and loss tolerant. Despite being constructed for qudits, our steering test is designed for single-detector measurements and is able to close the fair-sampling loophole in a time-efficient manner. We showcase the improvements over qubit-based systems by experimentally demonstrating quantum steering in up to 53 dimensions, free of the fair-sampling loophole, through simultaneous loss and noise conditions corresponding to 14.2-dB loss equivalent to 79 km of telecommunication fiber, and 36% of white noise. We go on to show how the use of high dimensions counterintuitively leads to a dramatic reduction in total measurement time, enabling a quantum steering violation almost 2 orders of magnitude faster obtained by simply doubling the Hilbert space dimension. Our work conclusively demonstrates the significant resource advantages that high-dimensional entanglement provides for quantum steering in terms of loss, noise, and measurement time, and opens the door toward practical quantum networks with the ultimate form of security.Received 26 April 2022Revised 29 September 2022Accepted 21 October 2022DOI:https://doi.org/10.1103/PhysRevX.12.041023Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement detectionEntanglement measuresNonlocalityQuantum communicationQuantum entanglementQuantum InformationAtomic, Molecular & Optical

Robust method for certifying genuine high-dimensional quantum steering with multimeasurement settings

Genuine high-dimensional (HD) quantum steering was recently proposed for certifying HD entanglement in the one-sided device-independent setting, as quantified by the Schmidt number [Phys. Rev. Lett. 126, 200404 (2021)PRLTAO0031-900710.1103/PhysRevLett.126.200404]. As one of the central challenges in the steering test is the tolerated noise threshold, here we develop a more robust method for certifying genuine HD steering in noisy environments. We derive genuine HD steering criteria using multiple mutually unbiased bases, surpassing the previous restriction of only two measurement settings. Although the present multisetting criteria are not tight, we theoretically show that they are more robust to noise than the tight two-setting criteria. To test the practicality of our method under realistic conditions, we report an experimental demonstration using photonic orbital angular momentum entangled states in dimensions d = 3 , 4 , 5 . Our work offers a more robust way to witness the entanglement dimension in practical one-sided device-independent quantum information processing.

Genuine High-Dimensional Quantum Steering.

High-dimensional quantum entanglement can give rise to stronger forms of nonlocal correlations compared to qubit systems, offering significant advantages for quantum information processing. Certifying these stronger correlations, however, remains an important challenge, in particular in an experimental setting. Here we theoretically formalize and experimentally demonstrate a notion of genuine high-dimensional quantum steering. We show that high-dimensional entanglement, as quantified by the Schmidt number, can lead to a stronger form of steering, provably impossible to obtain via entanglement in lower dimensions. Exploiting the connection between steering and incompatibility of quantum measurements, we derive simple two-setting steering inequalities, the violation of which guarantees the presence of genuine high-dimensional steering, and hence certifies a lower bound on the Schmidt number in a one-sided device-independent setting. We report the experimental violation of these inequalities using macropixel photon-pair entanglement certifying genuine high-dimensional steering. In particular, using an entangled state in dimension d=31, our data certifies a minimum Schmidt number of n=15.

Device-independent quantum authorization based on the Clauser-Horne-Shimony-Holt game

In the spirit of device-independent cryptography, we present a two-party quantum authorization primitive with non-locality as its fueling resource. Therein, users are attributed authorization levels granting them access to a private database accordingly. The authorization levels are encoded in the non-local resources distributed to the users, and subsequently confirmed by their ability to win CHSH games using such resources. We formalize the protocol, prove its security, and frame it in the device-independent setting employing the notion of CHSH self-testing via simulation. Finally, we provide a proof-of-concept implementation using the Qiskit open-source framework.

Computing conditional entropies for quantum correlations

The rates of quantum cryptographic protocols are usually expressed in terms of a conditional entropy minimized over a certain set of quantum states. In particular, in the device-independent setting, the minimization is over all the quantum states jointly held by the adversary and the parties that are consistent with the statistics that are seen by the parties. Here, we introduce a method to approximate such entropic quantities. Applied to the setting of device-independent randomness generation and quantum key distribution, we obtain improvements on protocol rates in various settings. In particular, we find new upper bounds on the minimal global detection efficiency required to perform device-independent quantum key distribution without additional preprocessing. Furthermore, we show that our construction can be readily combined with the entropy accumulation theorem in order to establish full finite-key security proofs for these protocols.

Maximal randomness from partially entangled states

We investigate how much randomness can be extracted from a generic partially entangled pure state of two qubits in a device-independent setting, where a Bell test is used to certify the correct functioning of the apparatus. For any such state, we first show that two bits of randomness are always attainable both if projective measurements are used to generate the randomness globally or if a nonprojective measurement is used to generate the randomness locally. We then prove that the maximum amount of randomness that can be generated using nonprojective measurements globally is restricted to between approximately 3.58 and 3.96 bits. The upper limit rules out that a bound of four bits potentially obtainable with extremal qubit measurements can be attained. We point out this is a consequence of the fact that nonprojective qubit measurements with four outcomes can only be self-tested to a limited degree in a Bell experiment.

Device-independent certification of multipartite entanglement using measurements performed in randomly chosen triads

We consider the problem of demonstrating non-Bell-local correlations by performing local measurements in randomly chosen triads, i.e., three mutually unbiased bases, on a multipartite Greenberger-Horne-Zeilinger state. Our main interest lies on investigating the feasibility of using these correlations to certify multipartite entanglement in a device-independent setting. In contrast to previous works, our numerical results up to the eight-partite scenario suggest that if each triad is randomly but uniformly chosen according to the Haar measure, one always (except possibly for a set of measure zero) finds Bell-inequality-violating correlations. In fact, a substantial fraction of these is even sufficient to reveal, in a device-independent manner, various higher-order entanglement. In particular, for the specific cases of three parties and four parties, our results---obtained from semidefinite programming---suggest that these randomly generated correlations always reveal, even in the presence of a non-negligible amount of white noise, the genuine multipartite entanglement possessed by these states. In other words, provided local calibration can be carried out to good precision, a device-independent certification of the genuine multipartite entanglement contained in these states can, in principle, also be carried out in an experimental situation without sharing a global reference frame.

Device-Independent Randomness Amplification and Privatization

Randomness is an essential resource in computer science. In most applications perfect, and sometimes private, randomness is needed, while it is not even clear that such a resource exists. It is well known that the tools of classical computer science do not allow us to create perfect and secret randomness from a single weak public source. Quantum physics, on the other hand, allows for such a process, even in the most paranoid cryptographic sense termed "quantum device-independent cryptography". In this work we propose and prove the security of a new device-independent protocol that takes any single public Santha-Vazirani source as input and creates a secret close to uniform string in the presence of a quantum adversary. Our work is the first to achieve randomness amplification with all the following properties: (1) amplification and "privatization" of a public Santha-Vazirani source with arbitrary bias (2) the use of a device with only two components (compared to polynomial number of components) (3) non-vanishing extraction rate and (4) maximal noise tolerance. In particular, this implies that our protocol is the first protocol that can possibly be implemented with reachable parameters. We are able to achieve these by combining three new tools: a particular family of Bell inequalities, a proof technique to lower bound entropy in the device-independent setting, and a special framework for quantum-proof multi-source extractors.

Certified Randomness From Steering Using Sequential Measurements

The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, i.e., we do not need to make assumptions about the devices used. Due to the work of Curchod et al. a single entangled two-qubit pure state can be used to produce arbitrary amounts of certified randomness. However, the obtaining of this randomness is experimentally challenging as it requires a large number of measurements, both projective and general. Motivated by these difficulties in the device-independent setting, we instead consider the scenario of one-sided device independence where certain devices are trusted, and others are not; a scenario motivated by asymmetric experimental set-ups such as ion-photon networks. We show how certain aspects of previous works can be adapted to this scenario and provide theoretical bounds on the amount of randomness that can be certified. Furthermore, we give a protocol for unbounded randomness certification in this scenario, and provide numerical results demonstrating the protocol in the ideal case. Finally, we numerically test the possibility of implementing this scheme on near-term quantum technologies, by considering the performance of the protocol on several physical platforms.

Upper bound on certifiable randomness from a quantum black-box device

Quantum theory allows for randomness generation in a device-independent setting, where no detailed description of the experimental device is required. Here we derive a general upper bound on the amount of randomness that can be generated in such a setting. Our bound applies to any black-box scenario, thus covering a wide range of scenarios from partially characterised to completely uncharacterised devices. Specifically, we prove that the number of random bits that can be generated is limited by the number of different input states that enter the measurement device. We show explicitly that our bound is tight in the simplest case. More generally, our work indicates that the prospects of generating a large amount of randomness by using high-dimensional (or even continuous variable) systems will be extremely challenging in practice.

Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing

The device-independent approach to physics is one where conclusions about physical systems (and hence of Nature) are drawn directly and solely from the observed correlations between measurement outcomes. This operational approach to physics arose as a byproduct of Bell’s seminal work to distinguish, via a Bell test, quantum correlations from the set of correlations allowed by local-hidden-variable theories. In practice, since one can only perform a finite number of experimental trials, deciding whether an empirical observation is compatible with some class of physical theories will have to be carried out via the task of hypothesis testing. In this paper, we show that the prediction-based-ratio method—initially developed for performing a hypothesis test of local-hidden-variable theories—can equally well be applied to test many other classes of physical theories, such as those constrained only by the nonsignaling principle, and those that are constrained to produce any of the outer approximation to the quantum set of correlations due to Navascués-Pironio-Acín. We numerically simulate Bell tests using hypothetical nonlocal sources of correlations to illustrate the applicability of the method in both the independent and identically distributed (i.i.d.) scenario and the non-i.i.d. scenario. As a further application, we demonstrate how this method allows us to unveil an apparent violation of the nonsignaling conditions in certain experimental data collected in a Bell test. This, in turn, highlights the importance of the randomization of measurement settings, as well as a consistency check of the nonsignaling conditions in a Bell test.

Reductions to IID in Device-independent Quantum Information Processing

The field of device-independent (DI) quantum information processing concerns itself with devising and analysing protocols, such as quantum key distribution, without referring to the quality of the physical devices utilised to execute the protocols. Instead, the analysis is based on the observed correlations that arise during a repeated interaction with the devices and, in particular, their ability to violate the so called Bell inequalities. Since the analysis of DI protocols holds irrespectively of the underlying physical device, it implies that any device can be used to execute the protocols: If the apparatus is of poor quality, the users of the protocol will detect it and abort; otherwise, they will accomplish their goal. This strong statement comes at a price-- the analysis of DI protocols is, a priori, extremely challenging. The thesis presents an approach that can be taken to simplify the analysis of DI information processing protocols. The idea is the following: Instead of analysing the most general device leading to the observed correlations, one should first analyse a significantly simpler device that, in each interaction with the user, behaves in an identical way, independently of all other interactions. We call such a device an independently and identically distributed (IID) device. As the next step, special techniques are used to prove that, without loss of generality, the analysis of the IID device implies similar results for the most general device. These are termed reductions to IID. We present two mathematical techniques that can be used as reductions to IID in the DI setting, each accompanied by a showcase-application that exemplifies the reduction's usage and benefits. Performing the analysis via a reduction to IID leads to simpler proofs and significant quantitive improvements, matching the tight results proven when analysing IID devices.

Maximal Randomness Generation from Steering Inequality Violations Using Qudits

We consider the generation of randomness based upon the observed violation of an Einstein-Podolsky-Rosen (EPR) steering inequality, known as one-sided device-independent randomness generation. Weshow that in the simplest scenario-involving only two parties and two measurements for the uncharacterised party with d outcomes-that there exist EPR steering inequalities whose maximal violation certifies maximal randomness generation, equal to log(d) bits. We further show that all pure partially entangled full-Schmidt-rank states in all dimensions can achieve maximal violation of these inequalities, and thus lead to maximal randomness generation in the one-sided device-independent setting. More generally, the amount of randomness that can be generated is given by a semidefinite program, which we use to study the behavior for nonmaximal violations of the inequalities.

Secrecy in Prepare-and-Measure Clauser-Horne-Shimony-Holt Tests with a Qubit Bound.

The security of device-independent (DI) quantum key distribution (QKD) protocols relies on the violation of Bell inequalities. As such, their security can be established based on minimal assumptions about the devices, but their implementation necessarily requires the distribution of entangled states. In a setting with fully trusted devices, any entanglement-based protocol is essentially equivalent to a corresponding prepare-and-measure protocol. This correspondence, however, is not generally valid in the DI setting unless one makes extra assumptions about the devices. Here we prove that a known tight lower bound on the min entropy in terms of the Clauser-Horne-Shimony-Holt Bell correlator, which has featured in a number of entanglement-based DI QKD security proofs, also holds in a prepare-and-measure setting, subject only to the assumption that the source is limited to a two-dimensional Hilbert space.

Anonymous quantum nonlocality.

We investigate the phenomenon of anonymous quantum nonlocality, which refers to the existence of multipartite quantum correlations that are not local in the sense of being Bell-inequality-violating but where the nonlocality is--due to its biseparability with respect to all bipartitions--seemingly nowhere to be found. Such correlations can be produced by the nonlocal collaboration involving definite subset(s) of parties but to an outsider, the identity of these nonlocally correlated parties is completely anonymous. For all n≥3, we present an example of an n-partite quantum correlation exhibiting anonymous nonlocality derived from the n-partite Greenberger-Horne-Zeilinger state. An explicit biseparable decomposition of these correlations is provided for any partitioning of the n parties into two groups. Two applications of these anonymous Greenberger-Horne-Zeilinger correlations in the device-independent setting are discussed: multipartite secret sharing between any two groups of parties and bipartite quantum key distribution that is robust against nearly arbitrary leakage of information.

Device-independent randomness extraction from an arbitrarily weak min-entropy source

Expansion and amplification of weak randomness plays a crucial role in many security protocols. Using quantum devices, such procedure is possible even without trusting the devices used, by utilizing correlations between outcomes of parts of the devices. We show here how to extract random bits with an arbitrarily low bias from a single arbitrarily weak min-entropy source in a device independent setting. To do this we use Mermin devices that exhibit super-classical correlations. Number of devices used scales polynomially in the length of the random sequence $n$. Our protocol is robust, it can tolerate devices that malfunction with a probability dropping polynomially in $n$ at the cost of a minor increase of the number of devices used.

Negativity as an estimator of entanglement dimension.

Among all entanglement measures negativity arguably is the best known and most popular tool to quantify bipartite quantum correlations. It is easily computed for arbitrary states of a composite system and can therefore be applied to discuss entanglement in an ample variety of situations. However, as opposed to logarithmic negativity, its direct physical meaning has not been pointed out yet. We show that the negativity can be viewed as an estimator of how many degrees of freedom of two subsystems are entangled. As it is possible to give lower bounds for the negativity even in a device-independent setting, it is the appropriate quantity to certify quantumness of both parties in a bipartite system and to determine the minimum number of dimensions that contribute to the quantum correlations.