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arXiv:0802.1633

Note on genuine multipartite classical correlations

Andrzej Grudka, Michał Horodecki, Paweł Horodecki, Ryszard Horodecki

Published Feb 12, 2008• 1 citation
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Abstract

We discuss the problem of coexistence of genuine quantum multipartite correlations and classical multipartite correlations. We introduce a postulate which any measure of genuine multipartite classical correlations should satisfy. We show that covariance does not satisfy this postulate. Finally we propose a definition of genuine multipartite correlations and illustrate it with examples.

DOI
10.48550/arxiv.0802.1633

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We discuss the problem of coexistence of genuine quantum multipartite correlations and classical multipartite correlations. We introduce a postulate which any measure of genuine multipartite classical correlations should satisfy. We show that covariance does not satisfy this postulate. Finally we propose a definition of genuine multipartite correlations and illustrate it with examples.
A lot of research has been done on multipartite correlations, but the problem of satisfactorily defining genuine multipartite correlations---those not trivially reducible to lower partite correlations---remains unsolved. In this paper we propose three reasonable postulates which each measure or indicator of genuine multipartite correlations (or genuine multipartite entanglement) should satisfy. We also introduce the concept of degree of correlations, which gives partial characterization of multipartite correlations. Then, we show that covariance does not satisfy two postulates and hence it cannot be used as an indicator of genuine multipartite correlations. Finally, we propose a candidate for a measure of genuine multipartite correlations based on the work that can be drawn from a local heat bath by means of a multipartite state.
We propose a measure for genuine multipartite correlations suited for the study of dynamics in open quantum systems. This measure is contextual in the sense that it depends on how information is read from the environment. It is used to study an interacting collective system of atoms undergoing phase transitions as external parameters are varied. We show that the steady state of the system can have a significant degree of genuine multipartite quantum and classical correlations and that the proposed measure can serve as a witness of critical behavior in quantum systems.
Genuine multpartite quantum nonlocality can be quantified by the communication cost needed to reproduce the nonlocal correlation by classical communication models. This prompts the question as to how one may provide such an operational characterization for the nonclassicality of local multipartite correlations arising from genuinely quantum states possessing quantum discord. To answer this question, we consider a classical simulation protocol where one of the parties pre-share a random variable with the other parties who may also share arbitrary randomness. We demonstrate that genuine nonclassicality of local multipartite correlations is necessary for implying genuine superlocality which is the requirement for a larger dimension of the random variable in the above classical simulation protocol than that of quantum state that can generate the nonclassical correlations.
Nonclassical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are n-particle states which do not exhibit n-partite correlations at all but still are genuinely n-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton experiment and analyze their properties in detail. Remarkably, even without multipartite correlations, these states do violate Bell inequalities showing that there is no classical, i.e., local realistic model describing their properties.