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arXiv:1310.1110 · Physical Review A

Role of correlations in the two-body-marginal problem

Lin Chen, Oleg Gittsovich, Kavan Kishore Modi, Marco Piani

Published Oct 13, 2014• 17 citations
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Abstract

The problem of deducing the global properties of correlations of tripartite quantum states based on the knowledge of their bipartite reductions is studied, shedding new light on the relation between local and global properties of quantum states and on the interplay between the classical and the quantum properties of correlations.
DOI
10.1103/physreva.90.042314

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We present an inequality on the purity of a bipartite state depending solely on the length difference of the local Bloch vectors. For two qubits this inequality is tight for all marginal states and so extends the previously known solution for the two-qubit marginal problem. With this inequality we construct a three-dimensional Bloch model of the two-qubit quantum state space in terms of Bloch lengths, providing a pleasing visualization of this high-dimensional state space. This allows to characterize quantum states by a strongly reduced set of parameters and to investigate the interplay between local properties of the marginal systems and global properties encoded in the correlations.