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arXiv:1511.08401 · Physical Review Letters

Genuinely Multipartite Entangled Quantum States with Fully Local Hidden Variable Models and Hidden Multipartite Nonlocality

Joseph Bowles, Jérémie Francfort, Mathieu Fillettaz, Flavien Hirsch, Nicolas Brunner

Published Mar 30, 2016• 67 citations
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Abstract

The relation between entanglement and nonlocality is discussed in the case of multipartite quantum systems. We show that, for any number of parties, there exist genuinely multipartite entangled states that admit a fully local hidden variable model, i.e., where all parties are separated. Hence, although these states exhibit the strongest form of multipartite entanglement, they cannot lead to Bell inequality violation considering general nonsequential local measurements. Then, we show that the nonlocality of these states can nevertheless be activated using sequences of local measurements, thus revealing genuine multipartite hidden nonlocality.

DOI
10.1103/physrevlett.116.130401

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The relation between entanglement and nonlocality is discussed in the case of multipartite quantum systems. We show that, for any number of parties, there exist genuinely multipartite entangled states that admit a fully local hidden variable model, i.e., where all parties are separated. Hence, although these states exhibit the strongest form of multipartite entanglement, they cannot lead to Bell inequality violation considering general nonsequential local measurements. Then, we show that the nonlocality of these states can nevertheless be activated using sequences of local measurements, thus revealing genuine multipartite hidden nonlocality.
Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that these two phenomena are inequivalent, as there exist entangled states of two parties that do not violate any Bell inequality. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such a relation in multipartite systems. We provide a general construction of genuinely multipartite entangled states that do not display genuinely multipartite nonlocality, thus proving that entanglement and nonlocality are inequivalent for any number of parties.
The nonlocality of certain quantum states can be revealed by using local filters before performing a standard Bell test. This phenomenon, known as hidden nonlocality, has been so far demonstrated only for a restricted class of measurements, namely, projective measurements. Here, we prove the existence of genuine hidden nonlocality. Specifically, we present a class of two-qubit entangled states, for which we construct a local model for the most general local measurements, and show that the states violate a Bell inequality after local filtering. Hence, there exist entangled states, the nonlocality of which can be revealed only by using a sequence of measurements. Finally, we show that genuine hidden nonlocality can be maximal. There exist entangled states for which a sequence of measurements can lead to maximal violation of a Bell inequality, while the statistics of nonsequential measurements is always local.
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.
We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.
It is a well-established fact that some quantum correlations can be nonlocal, meaning that they cannot be described by a local hidden variable model. Certain quantum correlations have a form of nonlocality so strong that they cannot be reproduced even by models having an arbitrarily small local hidden variable component. These correlations are called fully nonlocal and lead to Bell inequalities in which the maximum quantum value saturates the non-signaling bound. A well-known example of this effect, which is also referred to as quantum pseudo-telepathy or all-versus-nothing proofs of nonlocality, is the quantum distribution fulfilling the Peres-Mermin square, in which the underlying state is a 4×44\times44×4 dimensional maximally entangled state. Other examples of full nonlocality are known but, so far, all of them are for maximally entangled states and it is an open question whether maximal entanglement is necessary for full nonlocality. In this work, we first establish a link between full nonlocality and the concept of antidistinguishability of quantum states. We use this connection to show that in every bipartite d×dd\times dd×d Hilbert space, with d≥3d\geq3d≥3, there are non-maximally entangled states that are fully nonlocal. In fact, we derive simple sufficient conditions for full nonlocality that are only based on the smallest and largest Schmidt coefficients. We also show that in every dimension there exist pure entangled states that do not exhibit full nonlocality. Finally, we show that all pure entangled states can be activated to show full nonlocality in the many-copy scenario.
We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.