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| {information, entropy, channel} |
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Generalized Husimi Functions: Analyticity and Information Content
D. M. Appleby
abstract: The analytic properties of a class of generalized Husimi functions are
discussed, with particular reference to the problem of state reconstruction.
The class consists of the subset of Wodkiewicz's operational probability
distributions for which the filter reference state is a squeezed vacuum state.
The fact that the function is analytic means that perfectly precise knowledge
of its values over any small region of phase space provides enough information
to reconstruct the density matrix. If, however, one only has imprecise
knowledge of its values, then the amplification of statistical errors which
occurs when one attempts to carry out the continuation seriously limits the
amount of information which can be extracted. To take account of this fact a
distinction is made between explicate, or experimentally accessible
information, and information which is only present in implicate, experimentally
inaccessible form. It is shown that an explicate description of various aspects
of the system can be found localised on various 2 real dimensional surfaces in
complexified phase space. In particular, the continuation of the function to
the purely imaginary part of complexified phase space provides an explicate
description of the Wigner function.
- oai_identifier:
- oai:arXiv.org:quant-ph/9805054
- categories:
- quant-ph
- comments:
- 16 pages, 2 figures, AMS-latex. Replaced with published version
- arxiv_id:
- quant-ph/9805054
- journal_ref:
- J.Mod.Opt. 46 (1999) 825-841
- report_no:
- QMW-PH-98-21
- created:
- 1998-05-18
- updated:
- 1999-11-22
Full article ▸
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