Abstract
Quantum entanglement and non-locality are two special aspects of quantum correlations. The relationship between multipartite entanglement and non-locality is at the root of the foundations of quantum mechanics but there is still no general quantitative theory. In order to address this issue we analyze the relationship between tripartite non-locality and tripartite entanglement measure, called the three-tangle. We describe the states which give the extremal quantum values of a Bell-type inequality for a given value of the tripartite entanglement. Moreover, we show that such extremal states can be reached if one introduced an appropriate order induced by the three-π entanglement measure. Finally, we derive an analytical expression relating tripartite entanglement to the maximal violations of the Bell-type inequalities.
Highlights
Quantum entanglement and non-locality that is certified by the violation of Bell-type inequalities[1,2,3,4], are two special aspects of quantum theory, which distinguish quantum from the classical world
In this paper we investigate the problem of the restriction on the nonlocal correlations imposed on the tripartite qubit state with a given genuine tripartite entanglement (GTE)
We have derived a one-parameter family of states that yield the extremal quantum values of the Bell-type inequalities. Those states are known as tetrahedral states and reveal extremal properties with respect to the GHZ-states distillation and the GTE distribution, i.e., the highest difference in the estimation of GTE by mean of three-tangle and three-π
Summary
Quantum entanglement and non-locality that is certified by the violation of Bell-type inequalities[1,2,3,4], are two special aspects of quantum theory, which distinguish quantum from the classical world. The reverse implication is not true[7] As it was proven recently[8], for any number of parties N there exist states that do not violate any Bell inequality for genuine N-partite non-locality despite being genuinely N-partite entangled. Understanding the relation between these resources is one of the important problems of quantum theory from both fundamental and applied points of view While such relation has been successfully studied for the case of two qubits[9,10] and recently for pure two-qudit state[11], very little is known in the multipartite scenario. Correspondence and requests for materials should be addressed to www.nature.com/scientificreports/
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