Skip to main content

Quantum Statistical Inference

  • Chapter
Quantum Computation and Information

Part of the book series: Topics in Applied Physics ((TAP,volume 102))

  • 1729 Accesses

Abstract

We studied state estimation for several quantum statistical models and for estimation of unitary evolution. We also researched the hypothesis testing and state discrimination for entangled states from theoretical and experimental viewpoints. Moreover, we discussed the measurement theory. These results are reviewed in this Chapter.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. W. Helstrom: Minimum mean-square error estimation in quantum statistics, Phys. Lett. 25A, 101–102 (1967)

    ADS  Google Scholar 

  2. C. W. Helstrom: Quantum Detection and Estimation Theory (Academic, New York 1976)

    Google Scholar 

  3. K. Matsumoto: A new approach to the Cramer-Rao-type bound of the purestate model, J. Phys. A: Math. Gen. 35, 3111–3123 (2002)

    Article  MATH  ADS  Google Scholar 

  4. M. Hayashi: Asymptotic estimation theory for a finite dimensional pure state model, J. Phys. A: Math. Gen. 31, 4633–4655 (1998)

    Article  MATH  ADS  Google Scholar 

  5. M. Hayashi: On the second order asymptotics for pure states family, IEICE Transactions on Fundamentals A J88-A, 903–916 (2005) in Japanese

    Google Scholar 

  6. M. Hayashi: Estimation of squeezed state, in 9th International Conference on Squeezed States and Uncertainty Relations, (ICSSUR 2005) (Besancon, France 2005)

    Google Scholar 

  7. M. Hayashi: Lectures on quantum estimation and information, Workshop on Quantum Measurments and Operations for Criptography and Information Processing (2005) URL http://www.qubit.it/upcoming/gseminars/Hayashi/_SQUEEZED.PDF

    Google Scholar 

  8. M. Hayashi: Quantum Statistical Inferene and Quantum Correlation, vol. 80-4 (Bussei Kenkyu 2003) pp. 368–391, in Japanese

    Google Scholar 

  9. Y. Tsuda, K. Matsumoto, M. Hayashi: Disturbance of operation in quantum estimation for noised coherent light, in ERATO Conference on Quantum Information Science 2001 (EQIS01) (2001) p. 61

    Google Scholar 

  10. Y. Tsuda, K. Matsumoto: Quantum estimation for non-differentiable models, J. Phys. A: Math. Gen. 38, 1593–1613 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. D. G. Chapman, H. Robbins: Minimum variance estimation without regularity assumptions, Phys. Rev. Lett. 22, 581–586 (1951)

    MATH  MathSciNet  Google Scholar 

  12. J. M. Hammersley: On estimating restricted parameters, J. Roy. Statist. Soc. Ser. 12, 192–240 (1950)

    MATH  MathSciNet  Google Scholar 

  13. M. Hayashi: Quantum effect ob eigen-value estimation in quantum two-leve system, J. IPSJ 46(10), 2447–2467 (2005) in Japanese

    Google Scholar 

  14. M. Hendrych, M. Dusek, R. Filip, J. Fiurasek: Simple optical measurement of the overlap and fidelity of quantum states: An experiment, Phys. Lett. A 310, 95 (2003) quant-ph/0208091

    Article  MathSciNet  ADS  Google Scholar 

  15. A. Fujiwara: Estimation of SU(2) operation and dense coding: An information geometric approach, Phys. Rev. A 65, 012316 (2002)

    Article  ADS  Google Scholar 

  16. V. Bužek, R. Derka, S. Massar: Optimal quantum clocks, Phys. Rev. Lett. 82, 2207 (1999)

    Article  ADS  Google Scholar 

  17. M. Hayashi: Estimation of SU(2) action by using entanglement, Phys. Lett. A 354, 183–189 (2006) quant-ph/0407053

    Article  ADS  Google Scholar 

  18. E. Bagan, M. Baig, R. Muñoz-Tapia: Entanglement-assisted alignment of reference frames using a dense covariant coding, Phys. Rev. A 69, 050303(R) (2004)

    ADS  Google Scholar 

  19. E. Bagan, M. Baig, R. Muñoz-Tapia: Quantum reverse-engineering and reference-frame alignment without nonlocal correlations, Phys. Rev. A 70, 030301(R) (2004)

    Article  ADS  Google Scholar 

  20. G. Chiribella, G. M. D’Ariano, P. Perinotti, M. F. Sacchi: Efficient use of quantum resources for the transmission of a reference frame, Phys. Rev. Lett. 93, 180503 (2004)

    Article  ADS  Google Scholar 

  21. Y. Tsuda, K. Matsumoto, M. Hayashi: Hypothesis testing for a maximally entangled state, J. Phys. A: Math. Gen. quant-ph/0504203

    Google Scholar 

  22. M. Barbieri, F. D. Martini, G. Di Nepi, P. Mataloni, G. M. D’Ariano, C. Macchiavello: Experimental detection of entanglement with polarized photons, Phys. Rev. Lett. 91, 227901 (2003)

    Article  ADS  Google Scholar 

  23. S. Virmani, M. B. Plenio: Construction of extremal local positive-operator-valued measures under symmetry, Phys. Rev. A 67, 062308 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  24. J. Walgate, A. J. Short, L. Hardy, V. Vedral: Local distinguishability of multipartite orthogonal quantum states, Phys. Rev. Lett. 85, 4972 (2000)

    Article  ADS  Google Scholar 

  25. M. Horodecki, A. Sen De, U. Sen, K. Horodecki: Local indistinguishability: More nonlocality with less entanglement, Phys. Rev. Lett. 90, 047902 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  26. H. Fan: Distinguishability and indistinguishability by local operations and classical communication, Phys. Rev. Lett. 92, 177905 (2004)

    Article  ADS  Google Scholar 

  27. M. Owari, M. Hayashi: Local copying and local discrimination as a study for non-locality of a set, Phys. Rev. A submitted; quant-ph/0509062

    Google Scholar 

  28. M. Hayashi, D. Markham, M. Murao, M. Owari, S. Virmani: Bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication, Phys. Rev. Lett. 96, 040501 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  29. T. S. Han: Information-Spectrum Methods in Information Theory (Springer 2003) the original Japanese edition was published from Baifukan-Press, Tokyo, in 1998

    Google Scholar 

  30. H. Nagaoka, M. Hayashi: An information-spectrum approach to classical and quantum hypothesis testing, IEEE Trans. Info. Theor. (2002) submitted; LANL e-print quant-ph/0206185, (2002)

    Google Scholar 

  31. M. Hayashi: Hypothesis testing approach to quantum information theory, Quantum Information Theory Satellite Workshop (QIT-EQIS03) (2003)

    Google Scholar 

  32. M. Hayashi: Quantum Information: An Introduction (Springer 2006) the original Japanese edition was published from Saiensu-sha, Tokyo, in 2004

    Google Scholar 

  33. D. F. V. James, P. G. Kwiat, W. J. Munro, A. G. White: Measurement of qubits, Phys. Rev. A 64, 052312 (2001)

    Article  ADS  Google Scholar 

  34. K. Usami, Y. Nambu, Y. Tsuda, K. Matsumoto, K. Nakamura: Accuracy of quantum-state estimation utilizing Akaike’s information criterion, Phys. Rev. A 68, 022314 (2003)

    Article  ADS  Google Scholar 

  35. H. Akaike: Stochastic theory of minimal realization, IEEE Trans. Automat. Contr. 19, 667 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  36. K. Banaszek, G. M. D’Ariano, M. G. A. Paris, M. F. Sacchi: Maximum-likelihood estimation of the density matrix, Phys. Rev. A 61, 010304(R) (2000)

    ADS  Google Scholar 

  37. J. Rehácek, Z. Hradil, M. Jezek: Iterative algorithm for reconstruction of entangled states, Phys. Rev. A 63, 040303(R) (2001)

    Article  ADS  Google Scholar 

  38. M. Hayashi, B. Shi, A. Tomita, K. Mastumoto, Y. Tsuda, Y. Jinag: Hypothesis testing for an entangled state produced by spontaneous parametric down conversion, Phys. Rev. A submitted; quant-pW0603254

    Google Scholar 

  39. M. Hayashi, K. Matsumoto: Quantum universal veriable-length source cording, Phys. Rev. A 66, 022311 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  40. M. Hayashi, K. Matsumoto: Simple construction of quantum universal variable-length source coding, Quantum Informatin and Computation 2, 519–529 (2002)

    MathSciNet  MATH  Google Scholar 

  41. B. Schumacher: Quantum coding, Phys. Rev. A 51, 2738–2747 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  42. R. Jozsa, M. Horodecki, P. Horodecki, R. Horodecki: Universal quantum information compression, Phys. Rev. Lett. 81, 1714 (1998) quant-ph/9805017 (1998)

    Article  ADS  Google Scholar 

  43. K. Bostroem, T. Felbinger: Lossless quantum data compression and variablelength coding, Phys. Rev. A 65, 032313 (2002)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Hayashi, M. (2006). Quantum Statistical Inference. In: Imai, H., Hayashi, M. (eds) Quantum Computation and Information. Topics in Applied Physics, vol 102. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-33133-6_3

Download citation

Publish with us

Policies and ethics