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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Inequalities for the Ranks of Quantum States - Cad
ney \, J (University of Bristol)
DTSTART;TZID=Europe/London:20131030T140000
DTEND;TZID=Europe/London:20131030T150000
UID:TALK48574AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/48574
DESCRIPTION:We investigate relations between the ranks of marg
inals of multipartite quantum states. These are th
e Schmidt ranks across all possible bipartitions a
nd constitute a natural quantification of multipar
tite entanglement dimensionality. We show that the
re exist inequalities constraining the possible di
stribution of ranks. This is analogous to the case
of von Neumann entropy (lpha-R'enyi entropy for
lpha=1)\, where nontrivial inequalities constrain
ing the distribution of entropies (such as e.g. st
rong subadditivity) are known. It was also recentl
y discovered that all other lpha-R'enyi entropies
for $lphain(0\,1)p(1\,infty)$ satisfy only one
trivial linear inequality (non-negativity) and the
distribution of entropies for $lphain(0\,1)$ is
completely unconstrained beyond non-negativity. Ou
r result resolves an important open question by sh
owing that also the case of 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'enyi entropy are exceptional
ly interesting measures of entanglement in the mul
tipartite setting.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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