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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.

Statistical Model with Measurement Degree of Freedom and Quantum Physics