Online ISSN:1349-8606
Progress in Informatics  
No.8 March 2011  
Page 81-87  
Phase estimation with photon number constraint
Masahito HAYASHI

LINK [1] A. Luis and J. Perina,“Optimum phase-shift estimation and the quantum description of the phase difference,”Phys. Rev. A, vol.54, p.4564, 1996.

LINK [2] V. Buzek, R. Derka, and S. Massar, “Optimal quantum clocks,”Phys. Rev. Lett., vol.82, p.2207, 1999.

LINK [3] H. Imai and M. Hayashi,“Fourier Analytic Approach to Phase Estimation in Quantum Systems,”New J. Phys., vol.11, 043034, 2009.

LINK [4] A. Y. Kitaev, A. H. Shen, and M. N. Vyalyi,Classical and Quantum Computation, (Graduate Studies in Mathematics 47),American Mathematical Society, 2002.

LINK [5] V. Giovannetti, S. Lloyd, and L. Maccone,“Quantum-enhanced measurements: beating the standard quantum limit,”Science, vol.306, pp.1330-1336, 2004.

LINK [6] V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced“Quantum metrology”,”Phys. Rev. Lett., vol.96, 010401, 2006.

LINK [7] B. L. Higgins, D. W. Berry, S. D. Bartlett,H. M. Wiseman, and G. J. Pryde,“Entanglement-free Heisenberg-limited phase estimation,”Nature, vol.450, pp.393-396, 2007.

LINK [8] T. Nagata, R. Okamoto, J. L. O'Brien, K. Sasaki, and S. Takeuchi,“Beating the Standard Quantum Limit with Four-Entangled Photons,”Science, vol.316, no.5825, p.726, 2007.

LINK [9] R. Okamoto, H. F. Hofmann, T. Nagata, J. L. O'Brien, K. Sasaki, and S. Takeuchi,“Beating the standard quantum limit: phase super-sensitivity of N-photon interferometers,”New J. Phys., vol.10, 073033, 2008.

LINK [10] J. A. Jones, S. D. Karlen, J. Fitzsimons, A. Ardavan, S. C. Benjamin, G. A. D. Briggs, and J. J. L. Morton,“Magnetic Field Sensing Beyond the Standard Quantum Limit Using 10-Spin NOON States,”Science, vol.324, pp.1166-1168, 2009.

LINK [11] L. Pezze, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester,“Phase Detection at the Quantum Limit with Multiphoton Mach-Zehnder Interferometry,”Phys. Rev. Lett., vol.99, 223602, 2007.

LINK [12] M. Hayashi and K. Matsumoto,“Statistical model with measurement degree of freedom and quantum physics,”RIMS koukyuroku,no 1055, Kyoto, Kyoto University,p.96, 1998, In Japanese;M. Hayashi and K. Matsumoto,Asymptotic Theory of Quantum Statistical Inference,Ed M. Hayashi, Singapore, World Scientific, p.162, 2005,reprinted, English translation.

LINK [13] R. Gill and S. Massar, “State estimation for large ensembles,”Phys. Rev. A, vol.61, 042312, 2000.

LINK [14] A. Fujiwara,“Strong consistency and asymptotic efficiency for adaptive quantum estimation problems,”J. Phys. A: Math. Gen., vol.39, p.12489, 2006.

LINK [15] C. W. Helstrom,Quantum Detection and Estimation Theory,New York, Academic Press, 1976.

LINK [16] A. S. Holevo,Probabilistic and Statistical Aspects of Quantum Theory,Amsterdam, North-Holland, 1982,(Originally published in Russian 1980).

LINK [17] M. Hayashi,Quantum Information: An Introduction,Berlin, Springer, 2006.

LINK [18] A. S. Holevo,“Covariant measurements and uncertainty relations,”Rep. Math. Phys., vol.16, pp.385-400, 1979.

LINK [19] J. Hajek,“Local asymptotic minimax and admissibility in estimation,”Proc. Sixth Berkeley Symp. on Math. Statist. and Prob.,vol.1, Univ. of Calif. Press, pp.175-194, 1972.

LINK [20] M. Hayashi, “Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation,”to be published in Communications in Mathematical Physics,arXiv:1003.4575.

LINK [21] A. Fujiwara and H. Nagaoka,“Quantum Fisher metric and estimation for pure state models,”Phys. Lett. A, vol.201, p.119, 1995.