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

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.

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

References in corpus (1)

• Entanglement in thermal equilibrium states

Cited by in corpus (4)

• Eigenvalues, Separability and Absolute Separability of Two-Qubit States
• The Fate of Entanglement
• Entanglement quantifiers and phase transitions
• A simple spectral condition implying separability for states of bipartite quantum systems