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Open Systems & Information Dynamics

Activation of the Violation of Svetlichny Inequality for a Broad Class of States

Paweł Caban, Andrzej Molenda, Kamila Trzcińska

Published Dec 1, 2016• 1 citation
Publisher

Abstract

The fact that several copies of a local quantum state — when processed together — can generate a nonlocal correlation, i.e. the superactivation of quantum nonlocality, is a well-known feature of quantum mechanics. Most of research results focused strongly on the bipartite scenario. In this paper we show that the activation of violation of Svetlichny inequality, reported for the first time in our previous paper, is not an exceptional phenomenon but holds for a broad class of quantum states as well for pure as for mixed, noisy ones.

DOI
10.1142/s1230161216500189

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The fact that several copies of a local quantum state — when processed together — can generate a nonlocal correlation, i.e. the superactivation of quantum nonlocality, is a well-known feature of quantum mechanics. Most of research results focused strongly on the bipartite scenario. In this paper we show that the activation of violation of Svetlichny inequality, reported for the first time in our previous paper, is not an exceptional phenomenon but holds for a broad class of quantum states as well for pure as for mixed, noisy ones.
The phenomenon of superactivation of quantum nonlocality, i.e., the fact that several copies of a local quantum state when processed together can generate nonlocal correlations, has recently attracted much attention. However, this problem was considered mainly in a bipartite scenario (although some research in a multipartite case was also undertaken). In this paper we give explicit examples of activation of the violation of the Svetlichny inequality. The violation of the Svetlichny inequality is a sufficient condition of genuine tripartite nonlocality. We show that a number of pure GHZ-type states can be activated. We observe also that the amount of violation of the Svetlichny inequality by two copies of the GHZ state increases with an entanglement of a single copy of the state.
It is well known that quantum mechanics is incompatible with local realistic theories. Svetlichny showed, through the development of a Bell-like inequality, that quantum mechanics is also incompatible with a restricted class of nonlocal realistic theories for three particles where any two-body nonlocal correlations are allowed (Svetlichny 1987 Phys. Rev. D 35 3066). In the present work, we experimentally generate three-photon GHZ states to test Svetlichny's inequality. Our states are fully characterized by quantum state tomography using an overcomplete set of measurements and have a fidelity of (84±1)% with the target state. We measure a convincing, 3.6σ, violation of Svetlichny's inequality and rule out this class of restricted nonlocal realistic models.
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.
We find two two-qubit bipartite states ${\ensuremath{\rho}}_{1},{\ensuremath{\rho}}_{2}$ such that arbitrarily many copies of one or the other cannot exhibit nonlocal correlations in a two-setting--two-outcome Bell scenario. However, the bipartite state ${\ensuremath{\rho}}_{1}\ensuremath{\bigotimes}{\ensuremath{\rho}}_{2}$ violates the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).] by an amount of 2.023. We also identify a CHSH-local state $\ensuremath{\rho}$ such that ${\ensuremath{\rho}}^{\ensuremath{\bigotimes}2}$ is CHSH inequality-violating. The tools employed can be easily adapted to find instances of nonlocality activation in arbitrary Bell scenarios.