: この文書について...
: tokubetu1
: 結論
- 1
-
Amari, S.,
Differential-Geometrical Methods in Statistics,
Lecture Notes in Statistics, Vol. 28
Springer, Berlin, 1985.
- 2
-
Amari, S., and Nagaoka, H.,
Methods of Information Geometry,
AMS/OUP, 2000.
- 3
- Fu, J. C.,
Large sample point estimation:
A large devitation theory approach, Ann. stat., 10, (1982), 762-771.
- 4
- 藤原 彰夫,
量子状態の統計的推定理論,
東京大学大学院工学研究科計数工学専攻,修士論文, (1993).
- 5
-
Fujiwara, A., and Nagaoka, H.,
Quantum Fisher metric and estimation for pure state models,
Physics Letters 201A, (1995), 119-124.
- 6
-
Fujiwara, A., and Nagaoka, H.,
An estimation theoretical characterization of coherent states,
Journal of Mathematical Physics 40, (1999), 4227-4239.
- 7
- Hayashi, M.,
Asymptotics of Quantum Relative Entropy
From Representation Theoretical Viewpoint,
E-print http://xxx.lanl.gov/abs/quant-ph/9704040/ (1997).
- 8
- Hayashi, M.,
A Linear Programming Approach to
Attainable Cramer-Rao type bound and Randomness Conditions,
E-print http://xxx.lanl.gov/abs/quant-ph/9704044/.
- 9
- Hayashi, M.,
A Linear Programming Approach to Attainable Cramer-Rao type bound,
Quantum Communication, Computing, and Measurement,
(edited by Hirota, O., Holevo, A. S., and Caves, C. A.),
Plenum, New York, 1997, 99-108.
- 10
- Hayashi, M.,
Asymptotic estimation theory for a finite-dimensional pure
state model,
Journal of Physics A: Math. and Gen. 31, (1998), 4633-4655.
- 11
-
林正人,
量子推定理論における漸近的大偏差型評価について,
科研費シンポジウム「統計的推測理論とその情報論的側面」予稿集,
1998, 53-82.
- 12
-
林正人,
サンプル間の量子相関を用いた状態推定,
第7回「非平衡系の統計物理」シンポジウム報告集, 物性研究
Vol. 73 No. 4, (2000), 680-703.
- 13
- Hayashi, M.,
Asymptotic quantum theory for the thermal states family,
Quantum Communication, Computing, and Measurement 2,
(edited by Kumar, P., D'ariano, G. M., and Hirota, O.),
Plenum, New York, 2000, 99-104.
- 14
-
林正人,
量子推定における大偏差型評価,
日本数学会2000年度秋季総合分科会統計数学分科会講演アブストラクト
(2000), 85-86.
- 15
- Hayashi, M., and Sakaguchi, F.,
Subnormal operators regarded as generalized observables and
compound-system-type extension related to
,
Journal of Physics A: Math. and Gen. 33, (2000), 7793-7820.
- 16
-
林正人,松本啓史,
測定自由度をもつ統計モデルと量子力学,
数理解析研究所講究録 1055, (1998), 96-110.
- 17
-
林正人,松本啓史,
量子系における統計的推測の最近の発展,
日本応用数理学会誌, 掲載予定.
- 18
- Hayashi, M., in preparation.
- 19
- Helstrom, C. W.,
Minimum Mean-Square Error Estimation in Quantum Statistics,
Physics Letters 25A, (1967), 101-102.
- 20
- Helstrom, C. W.,
Quantum Detection and Estimation Theory,
Academic Press, New York, 1976.
- 21
- Holevo, A. S.,
Probabilistic and Statistical Aspects of Quantum Theory,
North-Holland, Amsterdam, 1982.
- 22
- Holevo, A. S.,
Covariant measurements and uncertainty relations,
Reports in Mathematical Physics 16, (1979) 385-400.
- 23
- 小林 昭七,
接続の微分幾何とゲージ理論, (裳華房, 1989).
- 24
- 松本啓史,
量子状態の幾何,
東京大学大学院工学研究科計数工学専攻,修士論文, (1995).
- 25
- Matsumoto, K.,
A new approach to the Cramer-Rao
type bound of the pure state model,
E-print http://xxx.lanl.gov/abs/quant-ph/9704044/ (1997).
- 26
- Matsumoto, K.,
Uhlmann's parallelism in quantum estimation theory,
E-print http://xxx.lanl.gov/abs/quant-ph/9711027/ (1997).
- 27
- Matsumoto, K.,
The asymptotic efficiency of the consistent esitmator,
Berry-Uhlmann's curvature, and quantum information geometry,
Quantum Communication, Computing, and Measurement 2,
(edited by Kumar, P., D'ariano, G. M., and Hirota, O.),
Plenum, New York, 2000, 105-110.
- 28
- Matsumoto, K.,
Berry's phase in view of quantum estimation theory,
and its intrinsic relation with the complex structure,
E-print http://xxx.lanl.gov/abs/quant-ph/0006076/ (2000).
- 29
-
Matsumoto, K.,
A geometrical approach to quantum estimation theory,
doctoral thesis,
Graduate School of Mathematical Sciences,
University of Tokyo (1997).
- 30
-
Nagaoka, H.,
On the Parameter Estimation Problem for Quantum Statistical Models,
第12回情報理論とその応用シンポジウム予稿集,
(1989), 577-582.
- 31
-
長岡浩司,
エルミート行列の同時対角化のある一般化と
その量子推定理論との関係について,
日本応用数理学会論文誌, vol. 1, No. 4,
(1991), 305-318.
- 32
- Yuen, H. P., and Lax, M.,
Multiple-Parameter Quantum Estimation and Measurement of
Nonselfadjoint Observables,
IEEE Trans. IT-19, (1973), 740-750.
Masahito Hayashi
平成13年7月10日