Spectral Conditions on the State of a Composite Quantum System Implying its Separability

Details Spectral Conditions on the State of a Composite Quantum System Implying its Separability Spectral Conditions on the State of a Composite Quantum System Implying its Separability

2005-05-09

arxiv.org/abs/quant-ph/0505044v3

Physics

Quantum Physics

Corrects 1. of Lemma 2, and the (under)statement of Proposition 7 of the earlier version 2

Scientific paper

10.1088/0305-4470/39/3/013

For any unitarily invariant convex function F on the states of a composite quantum system which isolates the trace there is a critical constant C such that F(w)<= C for a state w implies that w is not entangled; and for any possible D > C there are entangled states v with F(v)=D. Upper- and lower bounds on C are given. The critical values of some F's for qubit/qubit and qubit/qutrit bipartite systems are computed. Simple conditions on the spectrum of a state guaranteeing separability are obtained. It is shown that the thermal equilbrium states specified by any Hamiltonian of an arbitrary compositum are separable if the temperature is high enough.

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