论文信息 - Statistical Model with Measurement Degree of Freedom and Quantum Physics

Statistical Model with Measurement Degree of Freedom and Quantum Physics

This is an English translation of the manuscript which appeared in Surikaiseki Kenkyusho Kokyuroku No. 1055 (1998). The asymptotic efficiency of statistical estimate of unknown quantum states is discussed, both in adaptive and collective settings. Aaptive bounds are written in sigle letterized form, and collective bounds are written in limitting expression. Our arguments clarify mathematical regularity conditions.

Masahito Hayashi | Keiji Matsumoto

[1] H. Nagaoka. On the Relation between Kullback Divergence and Fisher Information: From Classical Systems to Quantum Systems , 2005 .

[2] Hiroshi Nagaoka,et al. On the Parameter Estimation Problem for Quantum Statistical Models , 2005 .

[3] W. Stinespring. Positive functions on *-algebras , 1955 .

[4] H. Yuen. Quantum detection and estimation theory , 1978, Proceedings of the IEEE.

[5] 松本啓史,et al. A geometrical approach to quantum estimation theory = 量子推定理論の幾何学的方法 , 1998 .

[6] E. L. Lehmann,et al. Theory of point estimation , 1950 .

[7] C. M. Care. Probabilistic and Statistical Aspects of Quantum Theory: North-Holland Series in Statistics and Probability Vol 1 , 1983 .

[8] M. Ozawa. Quantum measuring processes of continuous observables , 1984 .