Thursday, March 8, 2012

1203.1364 (Lin Chen et al.)

Properties and construction of extreme bipartite states having positive
partial transpose

Lin Chen, Dragomir Z. Djokovic
We investigate the set E of extreme points of the compact convex set of PPT states (i.e., the states having positive semidefinite partial transpose) of a bipartite MxN quantum system. Let E(M,N,r) denote the subset of E consisting of states of rank r which are supported on MxN. We show that for M,N>2 the sets E(M,N,M+N-2) are nonempty. On the other hand we show that for M,N>3 the sets E(M,N,N+1) are empty. It is known that the set E(M,N,MN) is empty, and we show that also the set E(M,N,MN-1) is empty. We divide the set of all states into the good and the bad states (the definition is too technical to be given here). We show that the good states have many good properties.
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