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Physics Letters A

Nonnegative mixed states in Weyl-Wigner-Moyal theory

JoséM. Garcia-Bondia, Joseph C. Várilly

Published Mar 1, 1988• 24 citations
Publisher
DOI
10.1016/0375-9601(88)91035-3

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CConsider a bipartite quantum system consisting of two subsystems A and B. The reduced density matrix ofA a is obtained by taking the partial trace with respect to B. In this work, we will show that the Wigner distribution of this reduced density matrix is obtained by integrating the total Wigner distribution with respect to the phase space variables corresponding to subsystem B. The proof we give is rigorous (as opposed to those found in the literature) and makes use of the Weyl--Wigner--Moyal phase space formalism. Our main result is applied to general Gaussian mixed states, of which it gives a particularly simple and precise description. We also briefly discuss the purification of a mixed state from the Wigner formalism point of view.
We present a complete review of the quantum-to-classical limit of open systems by means of the theory of decoherence and the use of the Weyl-Wigner-Moyal (WWM) transformation. We show that the analytical extension of the Hamiltonian provides a set of poles that can be used to (a) explain the non-unitary evolution of the relevant system and (b) completely define the set of preferred states that constitute the mixture into which the system decoheres: the Moving Preferred Basis. Moreover, we show that the WWM of these states are the best candidates to obtain the trajectories in the classical phase-space.