Keiji Matsumoto (ERATO, JST, Japan)
Presentations: Click_Here_1, Click_Here_2
http://www.qci.jst.go.jp/~keiji/
Talks:
1. Quantum estimation theory (Introduction)
Abstract :
The
theme of the talk is the efficiency of estimate of unknown quantum state.
Before
going into quantum state estimation, classical statistical estimation theory
is reviewed briefly,
to understand background knowledge. Especially,
we put weight on the asymptotic setting,
in which the large number of copies
of unknown states are available.
Besides, basian theory and other approaches
are briefly introduced.
2. First order asymptotic theory of quantum
estimation theory
Abstract :
The theme of the talk is the efficiency
of estimate of unknown quantum state.
Especially,
we consider the case when large number of copies of unknown states are
available.
In this case, error of estimate decrese in the second power
of the number of the copies,
and our interest is the coefficient of the
leading term.
In this way, we can construct surprisingly general theory.
Experimental aspects of the theory is also discussed.
References:
Fujiwara, A., and Nagaoka, H., Quantum Fisher metric and estimation for pure state models, Physics Letters 201A, (1995), 119-124.
Fujiwara, A., and Nagaoka, H., An estimation theoretical characterization of coherent states, Journal of Mathematical Physics 40 , (1999), 4227-4239.
Gill, R., and Massar, S., Phys. Rev. A 61 , 042312 (2000)
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, E-print http://xxx.lanl.gov/abs/quant-ph/9704044.
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.
Hayashi, M., Asymptotic estimation theory for a finite-dimensional pure state model, Journal of Physics A: Math. and Gen. 31 , (1998), 4633-4655.
Hayashi, M., Matsumoto, K., Statistical models with adaptive measurements and quantum mechanics, RIMS kokyuroku 1055 , (1998), 96-110.
Helstrom, C. W., Minimum Mean-Square Error Estimation in Quantum Statistics, Physics Letters 25A , (1967), 101-102.
Quantum Detection and Estimation Theory, Academic Press, New York, 1976.
Holevo, A. S., Probabilistic and Statistical Aspects of Quantum Theory, North_Holland, Amsterdam, 1982.
Massar, S., and Popescu, S., Phys. Rev. Lett. 74 1259 (1995).
Matsumoto, K., A new approach to the Cramer-Rao type bound of the pure state model, J. Phys. A35 3111-3123 (2002), E-print http://xxx.lanl.gov/abs/quant-ph/quant-ph/9704044 (1997).
Matsumoto, K., Uhlmann's parallelism in quantum estimation theory, E-print http://xxx.lanl.gov/abs/quant-ph/quant-ph/9711027 (1997).
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.
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/quant-ph/0006076 (2000).
Matsumoto, K., A geometrical approach to quantum estimation theory, doctoral thesis, Graduate School of Mathematical Sciences, University of Tokyo (1997).
Nagaoka, H., On the Parameter Estimation Problem for Quantum Statistical Models, SITA, (1989) 577-582.
Shapere, A., and Wilczek, F., GEOMETRIC PHASES IN PHYSICS, Advanced Series in Mathematical Physics, vol. 5, World Scientific (1989).
Uhlmann, A., Parallel transport and `Quantum holonomy' along density operators, Reports on Mathematical Physics, 24 , (1986), 229-240.
Yuen, H. P., and Lax, M., Multiple-Parameter Quantum Estimation and Measurement of Nonselfadjoint Observables, IEEE Trans. IT-19 , (1973), 740-750.