Separability and correlations in composite states based on entropy methods
Abstract
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine the entanglement and correlation properties guided by the corresponding calculations of concurrence. It is shown that the entropy difference between that of the composite and its marginal density matrices may be of arbitrary sign except under special circumstances when conditional probability can be defined appropriately. This ambiguity is a consequence of the fact that the overlap matrix elements of the eigenstates of the composite density matrix with those of its marginal density matrices also play important roles in the definitions of probabilities and the associated entropies, along with their respective eigenvalues. The general results are illustrated using pure and mixedstate density matrices of twoqubit systems. Two classes of density matrices are found for which the conditional probability can be defined: (1) density matrices with commuting decompositions and (2) those that are decohered in the representation where the density matrices of the marginals are diagonal. The first class of states encompass those whose separability is currently understood as due to particular symmetries of the states. The second are a class of states that are expected to be useful for understanding separability. Examples of entropy functionals of these decohered states including the crucial isospectral case are discussed.
 Publication:

Physical Review A
 Pub Date:
 August 2002
 DOI:
 10.1103/PhysRevA.66.022104
 arXiv:
 arXiv:quantph/0203124
 Bibcode:
 2002PhRvA..66b2104R
 Keywords:

 03.65.Ud;
 03.67.a;
 03.65.Ta;
 Entanglement and quantum nonlocality;
 Quantum information;
 Foundations of quantum mechanics;
 measurement theory;
 Quantum Physics
 EPrint:
 22 pages, 1 Table, 1 Figure