For two qubits and for general bipartite quantum systems, we give a simple spectral condition in terms of the ordered eigenvalues of the density matrix which guarantees that the corresponding state is separable.
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 e
ntangled states v with F(v)=D. Upper- and lower bounds on C are given. The critical values of some Fs 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.
Inspired by the realignment or computable cross norm criterion, we present a new result about the characterization of quantum entanglement. Precisely, an interesting class of inequalities satisfied by all separable states of a bipartite quantum syste
m is derived. These inequalities induce new separability criteria that generalize the realignment criterion.
A decomposition form is introduced in this report to establish a criterion for the bi-partite separability of Bell diagonal states. A such criterion takes a quadratic form of the coefficients of a given Bell diagonal states and can be derived via a s
imple algorithmic calculation of its invariants. In addition, the criterion can be extended to a quantum system of higher dimension.
In this article, we show a sufficient and necessary condition for locally distinguishable bipartite states via one-way local operations and classical communication (LOCC). With this condition, we present some minimal structures of one-way LOCC indist
inguishable quantum state sets. As long as an indistinguishable subset exists in a state set, the set is not distinguishable. We also list several distinguishable sets as instances.
We investigate the separability of arbitrary dimensional tripartite sys- tems. By introducing a new operator related to transformations on the subsystems a necessary condition for the separability of tripartite systems is presented.
M.E. Gabach Clement
,
,G.A. Raggio
.
(2006)
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"A simple spectral condition implying separability for states of bipartite quantum systems"
.
Guido A. Raggio
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