Pure State Correlations: Chords in Phase Space

Details Pure State Correlations: Chords in Phase Space Pure State Correlations: Chords in Phase Space

2004-10-17

arxiv.org/abs/quant-ph/0410129v1

Physics

Quantum Physics

16 pages, 4 figures

Scientific paper

10.1088/0305-4470/38/7/005

The intensity of the overlap of a quantum state with all its phase space translations defines its quantum correlations. In the case of pure states, these are invariant with respect to Fourier transformation. The overlaps themselves are here studied in terms of the Wigner function and its Fourier transform, i.e., the characteristic function or chord function. Unlike the Wigner function, the chord function need not be real, but eventual symmetry with respect to reflections about a phase space point may relate these representations. Semiclassical approximations for the "classical-like" region of small chords and for large chords are derived. These lead to an interpretation of the Fourier invariance in terms of conjugate chords. The interrelation of large and small (sub-Planck) phase space structures previously noted in the literature are thus reinterpreted.

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