Device-independent Quantum Information Research Articles

Custom Bell inequalities from formal sums of squares

Bell inequalities play a key role in certifying quantum properties for device-independent quantum information protocols. It is still a major challenge, however, to devise Bell inequalities tailored for an arbitrary given quantum state. Existing approaches based on sums of squares provide results in this direction, but they are restricted by the necessity of first choosing measurement settings suited to the state. Here, we show how the sum of square property can be enforced for an arbitrary target state by making an appropriate choice of nullifiers, which is made possible by leaving freedom in the choice of measurement. Using our method, we construct simple Bell inequalities for several families of quantum states, including partially entangled multipartite GHZ states and qutrit states. In most cases we are able to prove that the constructed Bell inequalities achieve self-testing of the target state. We also use the freedom in the choice of measurement to self-test partially entangled two-qubit states with a family of settings with two parameters. Finally, we show that some statistics can be self-tested with distinct Bell inequalities, hence obtaining new insight on the shape of the set of quantum correlations.

Tripartite Svetlichny test with measurement dependence

The Bell test, as an important method for detecting nonlocality, is widely used in device-independent quantum information processing tasks. The security of these tasks is based on an assumption called measurement independence. Since this assumption is difficult to be guaranteed in practical Bell tests, it is meaningful to consider the effect of reduced measurement independence (i.e., measurement dependence) on Bell tests. Some research studies have shown that nonlocality can be detected even if measurement dependence exists. However, the relevant results are all based on bipartite Bell tests, and the results for multipartite Bell tests are still missing. In this paper, we explore this problem in the tripartite Svetlichny test. By considering flexible lower and upper bounds on the degree of measurement dependence, we obtain the relation among measurement dependence, guessing probability, and the maximal value of Svetlichny inequality. Our results reveal the case in which genuine nonlocality is nonexistent; at this point, the outcomes of the Bell test cannot be applied in device-independent quantum information processing tasks.

Quantum correlations on the no-signaling boundary: self-testing and more

In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. Even though it is long-known that the set of correlations allowed in quantum theory lies strictly between the Bell-local set and the no-signaling set, many questions concerning the geometry of the quantum set remain unanswered. Here, we revisit the problem of when the boundary of the quantum set coincides with the no-signaling set in the simplest Bell scenario. In particular, for each Class of these common boundaries containing k zero probabilities, we provide a (5−k)-parameter family of quantum strategies realizing these (extremal) correlations. We further prove that self-testing is possible in all nontrivial Classes beyond the known examples of Hardy-type correlations, and provide numerical evidence supporting the robustness of these self-testing results. Candidates of one-parameter families of self-testing correlations from some of these Classes are identified. As a byproduct of our investigation, if the qubit strategies leading to an extremal nonlocal correlation are local-unitarily equivalent, a self-testing statement provably follows. Interestingly, all these self-testing correlations found on the no-signaling boundary are provably non-exposed. An analogous characterization for the set M of quantum correlations arising from finite-dimensional maximally entangled states is also provided. En route to establishing this last result, we show that all correlations of M in the simplest Bell scenario are attainable as convex combinations of those achievable using a Bell pair and projective measurements. In turn, we obtain the maximal Clauser-Horne-Shimony-Holt Bell inequality violation by any maximally entangled two-qudit state and a no-go theorem regarding the self-testing of such states.

Mutually Unbiased Measurements, Hadamard Matrices, and Superdense Coding

Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corresponding rank-1 projective measurements are ubiquitous in quantum information theory. In this work, we study a recently introduced generalisation of MUBs called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mutually unbiased measurements</i> (MUMs). These measurements inherit the essential property of complementarity from MUBs, but the Hilbert space dimension is no longer required to match the number of outcomes. This operational complementarity property renders MUMs highly useful for device-independent quantum information processing. It has been shown that MUMs are strictly more general than MUBs. In this work we provide a complete proof of the characterisation of MUMs that are direct sums of MUBs. We then construct new examples of MUMs that are not direct sums of MUBs. A crucial technical tool for this construction is a correspondence with quaternionic Hadamard matrices, which allows us to map known examples of such matrices to MUMs that are not direct sums of MUBs. Furthermore, we show that–in stark contrast with MUBs–the number of MUMs for a fixed outcome number is unbounded. Next, we focus on the use of MUMs in quantum communication. We demonstrate how any pair of MUMs with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> outcomes defines a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -dimensional superdense coding protocol. Using MUMs that are not direct sums of MUBs, we disprove a recent conjecture due to Nayak and Yuen on the rigidity of superdense coding, for infinitely many dimensions. The superdense coding protocols arising in the refutation reveal how shared entanglement may be used in a manner heretofore unknown.

Coherent activation of a steerability-breaking channel

The inevitable noise within one-sided device-independent quantum information tasks may completely break any steering resources. These noisy effects are characterized by the steerability breaking (SB) channels. In this work, we demonstrate the use of a control system that can superpose $N$ copies of the given SB channel to activate SB channels such that the channel becomes a non-SB one. In particular, we analytically and numerically show that the SB depolarizing and amplitude-damping channel can be coherently activated when $N\ensuremath{\ge}2$. In addition, for both cases, the channels can preserve more steerability when increasing $N$. Finally, we propose circuit models to implement our proposed approaches and present the simulation results.

Steerability criteria based on Heisenberg–Weyl observables

Einstein–Podolsky–Rosen (EPR) steering is an intermediate form of nonlocality which interpolates between entanglement and Bell nonlocality. It has been shown that EPR steerable states are fundamental resources for one-sided device-independent quantum information tasks. Nevertheless, distinguishing quantum steerable states from the unsteerable ones in general cases remains a big challenge under active studies. The generalized Bloch representation of density matrices in terms of the Heisenberg observables is a useful tool for analyzing characteristics of quantum systems and plays an important role in quantum information. In this work, the role of this representation in detection of EPR steering is studied. More specifically, based on the correlation matrices of the Heisenberg–Weyl observables, a family of steerability criteria for arbitrary dimensional bipartite systems are proposed. A large class of Hermitian operators, which can conveniently witness steering in some scenarios, are further provided. Finally, these criteria are illustrated through several examples, are compared with some existing ones, and their power and advantages are exhibited in certain cases.

Robust self-testing of multipartite Greenberger-Horne-Zeilinger-state measurements in quantum networks

Self-testing is an examination for characterizing unknown quantum devices based on correlations of observed statistics in a black-box scenario. With development of large-scale quantum networks, the requirement for self-testing multipartite entangled measurements has become very demanding. We develop here a general procedure for self-testing arbitrary generalized Greenberger-Horne-Zeilinger-state (GHZ-state) measurements which applies to any number of parties. Moreover, it turns out that the existing result for the three-qubit GHZ-state measurement is recovered as a special case. Our results will motivate operational certification of quantum devices related to device-independent quantum information tasks for various scenarios in complicated quantum networks.

Detecting Einstein-Podolsky-Rosen steering via correlation matrices

Einstein-Podolsky-Rosen (EPR) steering is a kind of quantum nonlocal correlation characterizing the ability of one party to remotely affect another party's state by local measurements. It is regarded as an essential resource for one-sided device-independent quantum information processing. Although identification of EPR steerable states has been widely studied, it remains a hard issue under arbitrary local measurements. In this paper, we propose a steerability criterion for arbitrary dimensional bipartite systems via correlation matrices of local observables. In particular, we apply the steering criterion to three classes of local measurements which are of special significance: local orthogonal observables, mutually unbiased measurements, and general symmetric informationally complete measurements. We obtain some useful criteria that are operational and experimentally testable. We further illustrate the criteria through several examples, compare them with some steering criteria in the literature, and exhibit their power and advantages in certain cases.

Complete classification of steerability under local filters and its relation with measurement incompatibility

Quantum steering is a central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables (SEO), first proposed to connect the problem of steerability and measurement incompatibility. We provide an efficient method to compute the extractable steerability that is maximal via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples.

Retrieving High-Dimensional Quantum Steering from a Noisy Environment with N Measurement Settings.

One of the most often implied benefits of high-dimensional (HD) quantum systems is to lead to stronger forms of correlations, featuring increased robustness to noise. Here, we experimentally demonstrate the n-setting linear HD quantum steering criterion. We verify the large violation of the steering inequalities without full-state tomography. The lower bound of the violation is 2.24±0.01 in 11 dimensions, exceeding the bound (V<2) of two-setting criteria. Hence, a higher strength of steering has been revealed. Moreover, we demonstrate the method for enhancing the noise robustness without increasing dimension, alternatively, by increasing measurement settings. Using the entanglement in 11 dimensions, we experimentally retrieve steering nonlocality with 63.4±1.4% isotropic noise fraction, surpassing the 50% limitation of two-setting criteria. Our Letter offers the potential for practical one-sided device-independent quantum information processing that tolerates the noisy environment, lossy detection, and transcends the present transmission distance limitation.

Quantifying Quantumness of Channels Without Entanglement

Quantum channels breaking entanglement, incompatibility, or nonlocality are defined as such because they are not useful for entanglement-based, one-sided device-independent, or device-independent quantum information processing, respectively. Here, we show that such breaking channels are related to complementary tests of macrorealism i.e., temporal separability, channel unsteerability, temporal unsteerability, and the temporal Bell inequality. To demonstrate this we first define a steerability-breaking channel, which is conceptually similar to entanglement and nonlocality-breaking channels and prove that it is identical to an incompatibility-breaking channel. A hierarchy of quantum non-breaking channels is derived, akin to the existing hierarchy relations for temporal and spatial quantum correlations. We then introduce the concept of channels that break temporal correlations, explain how they are related to the standard breaking channels, and prove the following results: (1) A robustness-based measure for non-entanglement-breaking channels can be probed by temporal nonseparability. (2) A non-steerability-breaking channel can be quantified by channel steering. (3) Temporal steerability and non-macrorealism can be used for, respectively, distinguishing unital steerability-breaking channels and nonlocality-breaking channels for a maximally entangled state. Finally, a two-dimensional depolarizing channel is experimentally implemented as a proof-of-principle example to demonstrate the hierarchy relation of non-breaking channels using temporal quantum correlations

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.

Ab initio experimental violation of Bell inequalities

The violation of a Bell inequality is the paradigmatic example of device-independent quantum information: The nonclassicality of the data is certified without the knowledge of the functioning of devices. In practice, however, all Bell experiments rely on the precise understanding of the underlying physical mechanisms. Given that, it is natural to ask: Can one witness nonclassical behavior in a truly black-box scenario? Here, we propose and implement, computationally and experimentally, a solution to this ab initio task. It exploits a robust automated optimization approach based on the stochastic Nelder-Mead algorithm. Treating preparation and measurement devices as black boxes, and relying on the observed statistics only, our adaptive protocol approaches the optimal Bell inequality violation after a limited number of iterations for a variety photonic states, measurement responses, and Bell scenarios. In particular, we exploit it for randomness certification from unknown states and measurements. Our results demonstrate the power of automated algorithms, opening a venue for the experimental implementation of device-independent quantum technologies.

Self-testing of a single quantum device under computational assumptions

Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system's state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device's state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.

Self-Testing Mutually Unbiased Bases in Higher Dimensions with Space-Division Multiplexing Optical Fiber Technology

In the device-independent quantum information approach, the implementation of a given task can be self-tested solely from the recorded statistics and without detailed models for the employed devices. Even though experimentally demanding, it provides appealing verification schemes for advanced quantum technologies that naturally fulfil the associated requirements. In this work, we experimentally study whether self-testing protocols can be adopted to certify the proper functioning of new quantum devices built with modern space-division multiplexing optical fiber technology. Specifically, we consider the prepare-and-measure protocol of M.~Farkas and J.~Kaniewski (Phys.~Rev.~A 99, 032316) for self-testing measurements corresponding to mutually unbiased bases (MUBs) in a dimension $d>2$. In our scheme, the state preparation and measurement stages are implemented with a multi-arm interferometer built with new multi-core optical fibers and related components. Due to the high-overlap of the interferometer's optical modes achieved with this technology, we are able to reach the required visibilities for self-testing the implementation of two four-dimensional MUBs. We also quantify two operational quantities of the measurements: (i) the incompatibility robustness, connected to Bell violations, and (ii) the randomness extractable from the outcomes. Since MUBs lie at the core of several quantum information protocols, our results are of practical interest for future quantum works relying on space-division multiplexing optical fibers.

Experimental observation of quantum nonlocality in general networks with different topologies

Nonlocal correlation plays an important role in device independent quantum information processing. The standard Bell nonlocality has been well studied with single local hidden variables, however the nonlocal correlations in general networks with several independent quantum sources and distant observers have been far less explored. Here, by using three independent entangled photon sources and recently constructed nonlinear Bell inequalities, we experimentally test the nonlocal correlations in the network scenario with different topologies. The violation of the inequalities can be obtained simply with separate measurements, which is much more favourable from the practical point of view. Our experiment results show a violation as 0.7779±0.0093 for the star network, and 0.7303±0.0024 for the chain network. Furthermore, we demonstrate that more measurement settings for each observer can bound more information against an eavesdropper.

Operational characterization of multipartite nonlocal correlations

Nonlocality, one of the most puzzling features of multipartite quantum correlation, has been identified as a useful resource for device-independent quantum information processing. Motivated by the resource theory of quantum entanglement recently an operational framework have been proposed by Gallego et al. [\href{https://doi.org/10.1103/PhysRevLett.109.070401}{Phys. Rev. Lett. 109, 070401 (2012)}] and Bancal et al. [\href{https://doi.org/10.1103/PhysRevA.88.014102}{Phys. Rev. A 88, 014102 (2013)}] that characterizes the nonlocal resource present in multipartite quantum correlations. While the bipartite no-signaling correlations allows a dichotomous classification -- local vs. nonlocal, in multipartite scenario the authors have shown existence of several types of nonlocality that are inequivalent under the proposed operational framework. In this work we present a finer characterization of multipartite no-signaling correlations based on the same operational framework. We also clarify a statement in Gallego et al.'s work that could be misinterpreted and make the conclusions of that work more precise here.

Bounding sets of sequential quantum correlations and device-independent randomness certification

An important problem in quantum information theory is that of bounding sets of correlations that arise from making local measurements on entangled states of arbitrary dimension. Currently, the best-known method to tackle this problem is the NPA hierarchy; an infinite sequence of semidefinite programs that provides increasingly tighter outer approximations to the desired set of correlations. In this work we consider a more general scenario in which one performs sequences of local measurements on an entangled state of arbitrary dimension. We show that a simple adaptation of the original NPA hierarchy provides an analogous hierarchy for this scenario, with comparable resource requirements and convergence properties. We then use the method to tackle some problems in device-independent quantum information. First, we show how one can robustly certify over 2.3 bits of device-independent local randomness from a two-quibt state using a sequence of measurements, going beyond the theoretical maximum of two bits that can be achieved with non-sequential measurements. Finally, we show tight upper bounds to two previously defined tasks in sequential Bell test scenarios.

Setting Up Experimental Bell Tests with Reinforcement Learning.

Finding optical setups producing measurement results with a targeted probability distribution is hard, as apriori the number of possible experimental implementations grows exponentially with the number of modes and the number of devices. To tackle this complexity, we introduce a method combining reinforcement learning and simulated annealing enabling the automated design of optical experiments producing results with the desired probability distributions. We illustrate the relevance of our method by applying it to a probability distribution favouring high violations of the Bell-Clauser-Horne-Shimony-Holt (CHSH) inequality. As a result, we propose new unintuitive experiments leading to higher Bell-CHSH inequality violations than the best currently known setups. Our method might positively impact the usefulness of photonic experiments for device-independent quantum information processing.

Self-testing of quantum systems: a review

Self-testing is a method to infer the underlying physics of a quantum experiment in a black box scenario. As such it represents the strongest form of certification for quantum systems. In recent years a considerable self-testing literature has developed, leading to progress in related device-independent quantum information protocols and deepening our understanding of quantum correlations. In this work we give a thorough and self-contained introduction and review of self-testing and its application to other areas of quantum information.