Spectral Conditions on the State of a Composite Quantum System Implying its Separability
Quantum Physics
2009-11-11 v3
Abstract
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.
Keywords
Cite
@article{arxiv.quant-ph/0505044,
title = {Spectral Conditions on the State of a Composite Quantum System Implying its Separability},
author = {G. A. Raggio},
journal= {arXiv preprint arXiv:quant-ph/0505044},
year = {2009}
}
Comments
Corrects 1. of Lemma 2, and the (under)statement of Proposition 7 of the earlier version 2