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arXiv:1709.01420 · Physical Review A

Measure-independent anomaly of nonlocality

S. Camalet

Published Nov 27, 2017• 13 citations
arXivHTMLPDF

Abstract

We show that any Bell local state with a hidden nonlocality that can be revealed by local filtering is more, or equally, entangled than nonlocal states. More precisely, it can be deterministically transformed into a nonlocal state by local operations and classical communication. For such a state, there is a clear anomaly of nonlocality for any measures of entanglement and nonlocality. Moreover, we prove that the hidden nonlocality of any bipartite state more, or equally, entangled than nonlocal states can be revealed by local operations and the sending of two one-bit messages, one in each direction. For some particular states, one bit of communication is even enough.

DOI
10.1103/physreva.96.052332

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•Jan 1, 2016•51 citations
We show that any Bell local state with a hidden nonlocality that can be revealed by local filtering is more, or equally, entangled than nonlocal states. More precisely, it can be deterministically transformed into a nonlocal state by local operations and classical communication. For such a state, there is a clear anomaly of nonlocality for any measures of entanglement and nonlocality. Moreover, we prove that the hidden nonlocality of any bipartite state more, or equally, entangled than nonlocal states can be revealed by local operations and the sending of two one-bit messages, one in each direction. For some particular states, one bit of communication is even enough.
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.
Nonlocal correlations arising from measurements on tripartite entangled states can be classified into two groups, one genuinely three-way nonlocal and other local with respect to some bipartition. Still, whether a genuinely tripartite entangled quantum state can exhibit genuine three-way nonlocality remains a challenging problem as far as measurement context is concerned. Here we introduce an approach in this regard. We consider three tripartite quantum states, none of which is genuinely three-way nonlocal in a specific Bell scenario (three parties, two measurements per party, two outcomes per measurement), but they can exhibit genuine three-way nonlocality when the initial states are subjected to stochastic local operations and classical communication. So, genuine three-way nonlocality is a resource which can be revealed by using a sequence of measurements.
A well-known manifestation of quantum entanglement is that it may lead to correlations that are inexplicable within the framework of a locally causal theory---a fact that is demonstrated by the quantum violation of Bell inequalities. The precise relationship between quantum entanglement and the violation of Bell inequalities is, however, not well understood. While it is known that entanglement is necessary for such a violation, it is not clear whether all entangled states violate a Bell inequality, even in the scenario where one allows joint operations on multiple copies of the state and local filtering operations before the Bell experiment. In this paper we show that all entangled states, or more precisely, all not-fully-separable states of arbitrary Hilbert space dimension and arbitrary number of parties, violate a Bell inequality when combined with another state which on its own cannot violate the same Bell inequality. This result shows that quantum entanglement and quantum nonlocality are in some sense equivalent, thus giving an affirmative answer to the aforementioned open question. It follows from our result that two entangled states that are apparently useless in demonstrating quantum nonlocality via a specific Bell inequality can be combined to give a Bell violation of the same inequality. Explicit examples of such activation phenomenon are provided.
Nonlocal quantum correlation is at the heart of the bizarre nature of quantum physics. While there are various classes of nonlocal quantum correlation, steerability of a quantum state by local measurements provides unique operational features. Here, we theoretically and experimentally investigate the ``hidden'' property of quantum steerability. In particular, we find that there are initially unsteerable states which can reveal the steerability by using local filters on individual quantum systems. It is remarkable that a certain set of local filters is more effective in revealing steerability than Bell nonlocality whereas there exists another set of filters that is more effective in revealing Bell nonlocality than steerability. This result suggests the structural difference between entanglement and steerability. Finally, we present a counterintuitive result that mixed states originating from nonmaximally pure entangled states can have hidden steerability while the mixed state from a maximally pure entangled state fails to show steerability.
Quantum nonlocality has different manifestations that, in general, are revealed by local measurements of the parts of a composite system. In this paper, we study nonlocality arising from a set of orthogonal states that cannot be perfectly distinguished by local operations and classical communication (LOCC). Such a set is deemed nonlocal, for a joint measurement on the whole system is necessary for perfect discrimination of the states with certainty. On the other hand, a set of orthogonal states that can be perfectly distinguished by LOCC is believed to be devoid of nonlocal properties. Here, we show that there exist orthogonal sets that are locally distinguishable but without local redundancy (i.e., they become nonorthogonal on discarding one or more subsystems) whose nonlocality can be activated by local measurements. In particular, a state chosen from such a set can be locally converted, with certainty, into another state, the identity of which can now only be ascertained by global measurement and no longer by LOCC. In other words, a locally distinguishable set without local redundancy may be locally converted into a locally indistinguishable set with certainty. We also suggest an application, namely, local hiding of information, that allows us to locally hide locally available information without losing any part. Once hidden, the information in its entirety can only be retrieved using entanglement.
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.