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Berry's Phase in the Quantum Estimation Theory, and Its Intrinsic Relation With the Complex Structure (1997)  (Make Corrections)  
Keiji Matsumoto



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Abstract: In this paper, it is pointed out that the Berry's phase is a good index of degree of manifestation of non-commutative nature in the quantum statistical model. Intrinsic relations between the `complex structure' of the Hilbert space and Berry's phase is also discussed. Keywords: Berry's phase quantum estimation theory, attainable Cramer-Rao typebound, complex structure, antiunitary operator 1 Department of Mathematical Engineering and Information Physics UniversityofTokyo, Bunkyo-ku,Tokyo 113,... (Update)

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BibTeX entry:   (Update)

@misc{ matsumoto-berrys,
  author = "Keiji Matsumoto",
  title = "Berry's Phase in the Quantum Estimation Theory, and Its Intrinsic Relation
    With the Complex Structure",
  url = "citeseer.ist.psu.edu/matsumoto97berrys.html" }
Citations (may not include all citations):
34   Quantum Detection and Estimation Theory (context) - Helstrom - 1976
29   Modern Quantum Mechanics (context) - Sakurai - 1985
13   Quantal phase factors accompanying adiabatic changes (context) - Berry - 1984
11   GEOMETRIC PHASES IN PHYSICS (context) - Shapere, Wilczek - 1989
9   Phase change during a cyclic quantum evolution (context) - Aharonov, Anandan - 1987
8   Minimum Mean-Square Error Estimation in Quantum Statistics (context) - Helstrom - 1967
6   Quantum measuring processes of continuous observables (context) - Ozawa - 1984
5   Quantum Fisher metric and estimation for pure state models (context) - Fujiwara, Nagaoka - 1995
4   On Fisher Information of Quantum Statistical Models (context) - Nagaoka - 1987
4   A new approach to the Cramer-Rao type bound of the pure stat.. (context) - Matsumoto - 1996
3   Uhlmann's parallelity in quantum estimation theory - Matsumoto - 1997
3   General Setting for Berry's Phase (context) - Samuel, Bhandari - 1988
2   A Geometrical Study in Quantum Information Systems (context) - Fujiwara - 1995
2   Holonomy, the quantum adiabatic theorem, and Berry's phase (context) - Simon - 1983
2   the Parameter Estimation Problem for Quantum Statistical Mod.. (context) - Nagaoka - 1989
1   private communication (context) - Fujiwara
1   Coherency in view of quantum estimation theory (context) - Fujiwara, Nagaoka - 1996
1   Effective Action for Adiabatic Process (context) - Kuratuji, Iida - 1985
1   Positive functions on C 3 -algebras (context) - Steinspring - 1955

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