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• W2036628293 abstract "We investigate relations between the ranks of marginals of multipartite quantum states. These are the Schmidt ranks across all possible bipartitions and constitute a natural quantification of multipartite entanglement dimensionality. We show that there exist inequalities constraining the possible distribution of ranks. This is analogous to the case of von Neumann entropy (alpha-R'enyi entropy for alpha=1), where nontrivial inequalities constraining the distribution of entropies (such as e.g. strong subadditivity) are known. It was also recently discovered that all other alpha-R'enyi entropies for $alphain(0,1)cup(1,infty)$ satisfy only one trivial linear inequality (non-negativity) and the distribution of entropies for $alphain(0,1)$ is completely unconstrained beyond non-negativity. Our result resolves an important open question by showing that also the case of alpha=0 (logarithm of the rank) is restricted by nontrivial linear relations and thus the cases of von Neumann entropy (i.e., alpha=1) and 0-R'enyi entropy are exceptionally interesting measures of entanglement in the multipartite setting." @default.
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• W2036628293 date "2014-07-01" @default.
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• W2036628293 title "Inequalities for the ranks of multipartite quantum states" @default.
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• W2036628293 doi "https://doi.org/10.1016/j.laa.2014.03.035" @default.
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