Energy-Sensitive and "Classical-like" Distances Between Quantum States

Details Energy-Sensitive and "Classical-like" Distances Between Quantum States Energy-Sensitive and "Classical-like" Distances Between Quantum States

1998-10-28

arxiv.org/abs/quant-ph/9810085v1

Phys.Scripta 59 (1999) 81-89

Physics

Quantum Physics

23 pages, LaTex, 2 eps figures, to appear in Physica Scripta

Scientific paper

10.1238/Physica.Regular.059a0008

We introduce the concept of the ``polarized'' distance, which distinguishes the orthogonal states with different energies. We also give new inequalities for the known Hilbert-Schmidt distance between neighbouring states and express this distance in terms of the quasiprobability distributions and the normally ordered moments. Besides, we discuss the distance problem in the framework of the recently proposed ``classical-like'' formulation of quantum mechanics, based on the symplectic tomography scheme. The examples of the Fock, coherent, ``Schroedinger cats,'' squeezed, phase, and thermal states are considered.

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