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SUMMARY:Inequalities for the Ranks of Quantum States - Cadney \, J (Univer
 sity of Bristol)
DTSTART:20131030T140000Z
DTEND:20131030T150000Z
UID:TALK48574@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We investigate relations between the ranks of marginals of mul
 tipartite quantum states. These are the Schmidt ranks across all possible 
 bipartitions and constitute a natural quantification of multipartite entan
 glement dimensionality. We show that there exist inequalities constraining
  the possible distribution of ranks. This is analogous to the case of von 
 Neumann entropy (lpha-R'enyi entropy for lpha=1)\, where nontrivial ineq
 ualities constraining the distribution of entropies (such as e.g. strong s
 ubadditivity) are known. It was also recently discovered that all other l
 pha-R'enyi entropies for $lphain(0\,1)p(1\,infty)$ satisfy only one triv
 ial linear inequality (non-negativity) and the distribution of entropies f
 or $lphain(0\,1)$ is completely unconstrained beyond non-negativity. Our 
 result resolves an important open question by showing that also the case o
 f lpha=0 (logarithm of the rank) is restricted by nontrivial linear relat
 ions and thus the cases of von Neumann entropy (i.e.\, lpha=1) and 0-R'en
 yi entropy are exceptionally interesting measures of entanglement in the m
 ultipartite setting.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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