Conciliation of bayes and pointwise quantum state estimation

Quantum Stochastics and Information: Statistics, Filtering, and Control

Volumn , Issue , 2008, Pages 239-261

  Gill, Richard D ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Cramer rao bounds; Statistical quantum information bounds; Van trees inequality

Indexed keywords

EID: 84969724143     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812832962_0011     Document Type: Chapter

References (15)

1. Bagan, E., M. A. Ballester, R. D. Gill, A. Monras, and R. Munoz-Tapia (2006a). Optimal full estimation of qubit mixed states. Phys. Rev. A 73 032301; arXiv:quant-ph/0510158.
2. Bagan, E., M. A. Ballester, R. D. Gill, R. Munoz-Tapia, and O. Romero- Isart (2006b). Separable-measurement estimation of density matrices and its fidelity gap with collective protocols. Phys. Rev. Lett. (in print); arXiv:quant-ph/0512177
3. Barndorff-Nielsen, O. E., R. D. Gill, and P. E. Jupp (2003). On quantum statistical inference. J. Roy. Statist. Soc. (B) 65, 775-816. With discussion and reply by the authors. arXiv:quant-ph/0307191.
4. Fuchs, C. A. (1995). Distinguishability and Accessible Information in Quantum theory. PhD thesis, University of New Mexico; arXiv:quant-ph/9601020.
5. Gill, R. D. (2001). Asymptotics in quantum statistics. In A. W. van der Vaart, M. de Gunst, and C. A. J. Klaassen (Eds.), State of the Art in Probability and Statistics (Leiden, 1999), Volume 36 of IMS Lecture notes Monogr. Ser., pp. 255-285. Beachwood, OH: Inst. Math. Statist. arXiv:math.ST/0405571.
6. Gill, R. D. and B. Y. Levit (1995). Applications of the Van Trees inequality: a Bayesian Cramer-Rao bound. Bernoulli 1, 59-79.
7. Gill, R. D. and S. Massar (2000). State estimation for large ensembles. Phys. Rev. A 61, 042312-042335. arXiv:quant-ph/9902063.
8. Guta, M. and J. Kahn (2006). Local asymptotic normality for qubit states. Phys. Rev. A 73, 052108. arXiv:quant-ph/0512075.
9. Hayashi, M. (1998). Asymptotic estimation theory for a finite dimensional pure state model. J. Phys. A 31, 4633-4655. arXiv:quant-ph/9704041.
10. Hayashi, M. (2003). Quantum estimation and quantum central limit theorem (in Japanese). Sugaku 55(4), 368-391. New, English translation: arXiv:quant-ph/0608198.
11. Hayashi, M. (2005) (editor). Asymptotic Theory of Quantum Statistical Inference: Selected Papers. Singapore: World Scientific.
12. Hayashi, M. and K. Matsumoto (2004). Asymptotic performance of optimal state estimation in quantum two level system. arXiv:quant-ph/0411073.
13. Holevo, A. S. (1982). Probabilistic and Statistical Aspects of Quantum Theory. Amsterdam: North-Holland. First appeared, in Russian, 1980.
14. Matsumoto, K. (2002). A new approach to the Cramer-Rao-type bound of the pure state model. J. Phys. A 35, 3111-3123. arXiv:quant-ph/9711008.
15. van Trees, H. (1968). Detection, Estimation and Modulation Theory, Part 1. New York: Wiley.