On the parameter estimation problem for quantum statistical models

Asymptotic Theory of Quantum Statistical Inference: Selected Papers

Volumn , Issue , 2005, Pages 125-132

  Nagaoka, Hiroshi ^a  

^a UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

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Indexed keywords

EID: 84967663396     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812563071_0011     Document Type: Chapter

References (11)

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2. S. Eguchi, "Second order efficiency of minimum contrast estimators in a curved exponential family," Ann. Statist., 11, 793-803 (1983).
3. C.W. Helstrom, "Minimum mean-square error estimation in quantum statistics," Phys. Lett., 25A, 101-102 (1967).
4. C.W. Helstrom, Quantum detection and estimation theory, Academic Press, New York, 1976.
5. A.S. Holevo, "Noncommutative analogues of the Cramér-Rao inequality in the quantum measurement theory," In Lecture Notes in Math., 550, 194-222 (1976).
6. A.S. Holevo, Probabilistic and statistical aspects of quantum theory, North- Holland, 1982.
7. R.S. Ingarden, et al., "Information geometry of quantum statistical systems," Tesor, N.S., 37, 105-111 (1982).
8. H. Nagaoka, "A new approach to Cramér-Rao bounds for quantum state estimation," IEICE Technical Report, 89, 228, IT 89-42, 9-14, (1989). (Chap. 8. in this book)
9. H. Nagaoka and S. Amari, "Differential geometry of smooth families of probability distributions," Math.Eng. Tech. Rep. 82-7, Univ. Tokyo (1982).
10. H. Umegaki, "Conditional expectation in an operator algebra, III," Kodai Math. Sem. Rep., 11, 51-64 (1959).
11. H.P. Yuen and M. Lax, "Multiple-parameter quantum estimation and measurement of non-selfadjoint observables," IEEE Trans. Inform. Theory, 19, 740-750 (1973).