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Gaussian Density Matrices: Quantum Analogs of Classical States
Author(s) -
Mann A.,
Revzen M.
Publication year - 1993
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190410503
Subject(s) - classical limit , gaussian , quantum state , quantum , beam splitter , quantum limit , phase space , quantum mechanics , density matrix , coherent states , limit (mathematics) , zero (linguistics) , physics , mathematical physics , mathematics , statistical physics , mathematical analysis , laser , linguistics , philosophy
We study quantum analogs of classical situations, i.e. quantum states possessing some specific classical attribute(s). These states seem quite generally, to have the form of gaussian density matrices. Such states can always be parametrized as thermal squeezed states (TSS). We consider the following specific cases: (a) Two beams that are built from initial beams which passed through a beam splitter cannot, classically, be distinguished from (appropriately prepared) two independent beams that did not go through a splitter. The only quantum states possessing this classical attribute are TSS. (b) The classical Cramer's theorem was shown to have a quantum version (Hegerfeldt). Again, the states here are Gaussian density matrices. (c) The special case in the study of the quantum version of Cramer's theorem, viz. when the state obtained after partial tracing is a pure state, leads to the conclusion that all states involved are zero temperature limit TSS. The classical analog here are gaussians of zero width, i.e. all distributions are δ functions in phase space.