Correlations, Bell Inequality Violation & Quantum Entanglement

It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation.Comment: PhD Thesis (176 pages). This thesis contains (1) a pedagogical review of the field (2) results previously reported in quant-ph/0604045, quant-ph/0608128, quant-ph/0703268, arXiv:0710.5350 (3) some relevant details omitted from these publications (4) a formal proof of equivalence between the class of CGLMP inequalities and the I_{22dd} inequalitie

A resource theory of quantum memories and their faithful verification with minimal assumptions

We provide a complete set of game-theoretic conditions equivalent to the existence of a transformation from one quantum channel into another one, by means of classically correlated pre/post processing maps only. Such conditions naturally induce tests to certify that a quantum memory is capable of storing quantum information, as opposed to memories that can be simulated by measurement and state preparation (corresponding to entanglement-breaking channels). These results are formulated as a resource theory of genuine quantum memories (correlated in time), mirroring the resource theory of entanglement in quantum states (correlated spatially). As the set of conditions is complete, the corresponding tests are faithful, in the sense that any non entanglement-breaking channel can be certified. Moreover, they only require the assumption of trusted inputs, known to be unavoidable for quantum channel verification. As such, the tests we propose are intrinsically different from the usual process tomography, for which the probes of both the input and the output of the channel must be trusted. An explicit construction is provided and shown to be experimentally realizable, even in the presence of arbitrarily strong losses in the memory or detectors.Comment: Addition of a quantitative study of memories as resources, and reformulated part of the results in that ligh

Quantifying multipartite nonlocality via the size of the resource

The generation of (Bell-)nonlocal correlations, i.e., correlations leading to the violation of a Bell-like inequality, requires the usage of a nonlocal resource, such as an entangled state. When given a correlation (a collection of conditional probability distributions) from an experiment or from a theory, it is desirable to determine the extent to which the participating parties would need to collaborate nonlocally for its (re)production. Here, we propose to achieve this via the minimal group size (MGS) of the resource, i.e., the smallest number of parties that need to share a given type of nonlocal resource for the above-mentioned purpose. In addition, we provide a general recipe --- based on the lifting of Bell-like inequalities --- to construct MGS witnesses for non-signaling resources starting from any given ones. En route to illustrating the applicability of this recipe, we also show that when restricted to the space of full-correlation functions, non-signaling resources are as powerful as unconstrained signaling resources. Explicit examples of correlations where their MGS can be determined using this recipe and other numerical techniques are provided.Comment: 8+3 pages, 2 figures, 2 theorems + 1 corollary; comments very welcomed

All bipartite entangled states display some hidden nonlocality

We show that a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality can be demonstrated in a certain kind of Bell experiment for all bipartite entangled states. Our protocol allows local filtering measurements and involves shared ancilla states that do not themselves violate CHSH. Our result follows from two main steps. We first provide a simple characterization of the states that violate the CHSH-inequality after local filtering operations in terms of witness-like operators. Second, we prove that for each entangled state $\sigma$, there exists another state $\rho$ not violating CHSH, such that $\rho\otimes\sigma$ violates CHSH. Hence, in this scenario, $\sigma$ cannot be substituted by classical correlations without changing the statistics of the experiment; we say that $\sigma$ is not simulable by classical correlations and our result is that entanglement is equivalent to non-simulability.Comment: 5 pages, 1 figur

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 Navascu\'es-Pironio-Ac\'{\i}n. 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.Comment: 10 pages, 1 figure, 3 tables (essentially the published version with simplified discussion and clearer presentation of results

Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations

In a recent work [Phys. Rev. Lett. 116, 240401 (2016)], a framework known by the name of "assemblage moment matrices" (AMMs) has been introduced for the device-independent quantification of quantum steerability and measurement incompatibility. In other words, even with no assumption made on the preparation device nor the measurement devices, one can make use of this framework to certify, directly from the observed data, the aforementioned quantum features. Here, we further explore the framework of AMM and provide improved device-independent bounds on the generalized robustness of entanglement, the incompatibility robustness and the incompatibility weight. We compare the tightness of our device-independent bounds against those obtained from other approaches. Along the way, we also provide an analytic form for the generalized robustness of entanglement for an arbitrary two-qudit isotropic state. When considering a Bell-type experiment in a tri- or more-partite scenario, we further show that the framework of AMM provides a natural way to characterize a superset to the set of quantum correlations, namely, one which also allows post-quantum steering.Comment: 17 pages, 6 figures. Comments welcome

Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing

We introduce the concept of assemblage moment matrices, i.e., a collection of matrices of expectation values, each associated with a conditional quantum state obtained in a steering experiment. We demonstrate how it can be used for quantum states and measurements characterization in a device-independent manner, i.e., without invoking any assumption about the measurement or the preparation device. Specifically, we show how the method can be used to lower bound the steerability of an underlying quantum state directly from the observed correlation between measurement outcomes. Combining such device-independent quantifications with earlier results established by Piani and Watrous [Phys. Rev. Lett. 114, 060404 (2015)], our approach immediately provides a device-independent lower bound on the generalized robustness of entanglement, as well as the usefulness of the underlying quantum state for a type of subchannel discrimination problem. In addition, by proving a quantitative relationship between steering robustness and the recently introduced incompatibility robustness, our approach also allows for a device-independent quantification of the incompatibility between various measurements performed in a Bell-type experiment. Explicit examples where such bounds provide a kind of self-testing of the performed measurements are provided.Comment: The core of these results were already presented at the Workshop on Quantum Nonlocality, Causal Structure and Device-independent Quantum Information on 14/12/2016; v2: closely approximates journal version; v3: title is updated as journal versio