Region Operators of Wigner Function: Transformations, Realizations and Bounds

Details Region Operators of Wigner Function: Transformations, Realizations and Bounds Region Operators of Wigner Function: Transformations, Realizations and Bounds

2005-10-18

arxiv.org/abs/quant-ph/0510140v1

Physics

Quantum Physics

16 pages, 4 figures. Hurst Bracken Festschrift, Reports of Mathematical Physics, Feb 2006, to appear

Scientific paper

10.1016/S0034-4877(06)80009-1

An integral of the Wigner function of a wavefunction |psi >, over some region S in classical phase space is identified as a (quasi) probability measure (QPM) of S, and it can be expressed by the |psi > average of an operator referred to as the region operator (RO). Transformation theory is developed which provides the RO for various phase space regions such as point, line, segment, disk and rectangle, and where all those ROs are shown to be interconnected by completely positive trace increasing maps. The latter are realized by means of unitary operators in Fock space extended by 2D vector spaces, physically identified with finite dimensional systems. Bounds on QPMs for regions obtained by tiling with discs and rectangles are obtained by means of majorization theory.

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