Quantum nonlocality does not imply entanglement distillability

Activation of Nonlocality in Bound Entanglement

We discuss the relation between entanglement and nonlocality in the hidden nonlocality scenario. Hidden nonlocality signifies nonlocality that can be activated by applying local filters to a particular state that admits a local hidden-variable model in the Bell scenario. We present a fully biseparable three-qubit bound entangled state with a local model for the most general (nonsequential) measurements. This proves for the first time that bound entangled states can admit a local model for general measurements. We furthermore show that the local model breaks down when suitable local filters are applied. Our results demonstrate the first example of activation of nonlocality in bound entanglement. Hence, we show that genuine hidden nonlocality does not imply entanglement distillability.

Quantum Correlations and Quantum Non-Locality: A Review and a Few New Ideas

In this paper we make an extensive description of quantum non-locality, one of the most intriguing and fascinating facets of quantum mechanics. After a general presentation of several studies on this subject dealing with different but connected facets of quantum non-locality, we consider if this, and the friction it carries with special relativity, can eventually find a “solution” by considering higher dimensional spaces.

Revealing nonclassicality beyond Gaussian states via a single marginal distribution

A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential-a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurement-axis-independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine non-Gaussianity under a CV measurement.

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.

Steering bound entangled States: a counterexample to the stronger Peres conjecture

Quantum correlations are at the heart of many applications in quantum information science and, at the same time, they form the basis for discussions about genuine quantum effects and their difference to classical physics. On one hand, entanglement theory provides the tools to quantify correlations in information processing and many results have been obtained to discriminate useful entanglement, which can be distilled to a pure form, from bound entanglement, being of limited use in many applications. On the other hand, for discriminating quantum phenomena from their classical counterparts, Schrödinger and Bell introduced the notions of steering and local hidden variable models. We provide a method to generate systematically bound entangled quantum states which can still be used for steering and, therefore, to rule out local hidden state models. This sheds light on the relations between the various views on quantum correlations and disproves a widespread conjecture known as the stronger Peres conjecture. For practical applications, it implies that even the weakest form of entanglement can be certified in a semidevice independent way.

Certifying separability in symmetric mixed states of N qubits, and superradiance

Separability criteria are typically of the necessary, but not sufficient, variety, in that satisfying some separability criterion, such as positivity of eigenvalues under partial transpose, does not strictly imply separability. Certifying separability amounts to proving the existence of a decomposition of a target mixed state into some convex combination of separable states; determining the existence of such a decomposition is "hard." We show that it is effective to ask, instead, if the target mixed state "fits" some preconstructed separable form, in that one can generate a sufficient separability criterion relevant to all target states in some family by ensuring enough degrees of freedom in the preconstructed separable form. We demonstrate this technique by inducing a sufficient criterion for "diagonally symmetric" states of N qubits. A sufficient separability criterion opens the door to study precisely how entanglement is (not) formed; we use ours to prove that, counterintuitively, entanglement is not generated in idealized Dicke model superradiance despite its exemplification of many-body effects. We introduce a quantification of the extent to which a given preconstructed parametrization comprises the set of all separable states; for "diagonally symmetric" states our preconstruction is shown to be fully complete. This implies that our criterion is necessary in addition to sufficient, among other ramifications which we explore.

Device-independent entanglement quantification and related applications

We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on the observed data only but independent of any quantum description of the employed devices. Some of the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell inequality or the Svetlichny inequality, are shown to be tight. Besides, device-independent entanglement quantification can serve as a basis for numerous tasks. We show in particular that our method provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device-independent entanglement witnesses involving an arbitrary number of parties.