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arXiv:1409.3679 · Scientific Reports

Quantum correlation exists in any non-product state

Yu Guo, Shengjun Wu

Published Dec 1, 2014• 22 citations
arXivHTMLPDF

Abstract

Simultaneous existence of correlation in complementary bases is a fundamental feature of quantum correlation, and we show that this characteristic is present in any non-product bipartite state. We propose a measure via mutually unbiased bases to study this feature of quantum correlation, and compare it with other measures of quantum correlation for several families of bipartite states.

DOI
10.1038/srep07179

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Simultaneous existence of correlation in complementary bases is a fundamental feature of quantum correlation, and we show that this characteristic is present in any non-product bipartite state. We propose a measure via mutually unbiased bases to study this feature of quantum correlation, and compare it with other measures of quantum correlation for several families of bipartite states.
An essential feature of genuine quantum correlation is the simultaneous existence of correlation in complementary bases. We reveal this feature of quantum correlation by defining measures based on invariance under a basis change. For a bipartite quantum state, the classical correlation is the maximal correlation present in a certain optimum basis, while the quantum correlation is characterized as a series of residual correlations in the mutually unbiased bases. Compared with other approaches to quantify quantum correlation, our approach gives information-theoretical measures that directly reflect the essential feature of quantum correlation.
One of the essential features of quantum mechanics is that most pairs of observables cannot be measured simultaneously. This phenomenon manifests itself most strongly when observables are related to mutually unbiased bases. In this paper, we shed some light on the connection between mutually unbiased bases and another essential feature of quantum mechanics, quantum entanglement. It is shown that a complete set of mutually unbiased bases of a bipartite system contains a fixed amount of entanglement, independent of the choice of the set. This has implications for entanglement distribution among the states of a complete set. In prime-squared dimensions we present an explicit experiment-friendly construction of a complete set with a particularly simple entanglement distribution. Finally, we describe the basic properties of mutually unbiased bases composed of product states only. The constructions are illustrated with explicit examples in low dimensions. We believe that the properties of entanglement in mutually unbiased bases may be one of the ingredients to be taken into account to settle the question of the existence of complete sets. We also expect that they will be relevant to applications of bases in the experimental realization of quantum protocols in higher-dimensional Hilbert spaces.
We introduce measures of multipartite quantum correlations based on classical correlations in mutually unbiased bases. These classical correlations are measured in terms of the classical mutual information, which has a clear operational meaning. We present sufficient conditions under which these measures are maximized. States that have previously been shown to be particularly important in the context of local operations and classical communication fulfill these conditions and therefore maximize the correlation measures. In addition, we show how the introduced measures can be used to detect high-dimensional tripartite entanglement by using only a few local measurements.
This paper studies the quantification and structural properties of quantum average correlation based on average coherence. Motivated by two mathematically equivalent approaches to define average coherence: one by averaging over complete sets of mutually unbiased bases, and the other by integrating over all orthogonal bases under the Haar measure, we define an average correlation for bipartite systems as the difference between global and local skew information. This correlation measure is shown to satisfy essential properties including non negativity, contractivity under local quantum channels, and local unitary invariance. We further prove the equivalence between the average correlation defined via mutually unbiased bases and that defined via unitary groups. Finally, we derive a complementarity relation that connects wave-particle duality with the average correlation between a system and its environment.
We investigate correlations among complementary observables. In particular, we show how to take advantage of mutually unbiased bases for the efficient detection of entanglement in arbitrarily high-dimensional, multipartite, and continuous-variable quantum systems. The introduced entanglement criteria are relatively easy to implement experimentally since they require only a few local measurement settings. In addition, we establish a link between the separability problem and the maximum number of mutually unbiased bases---opening an additional avenue in this long-standing open problem.