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A Linear Programming Approach to Attainable Cramér-Rao Type Bounds

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Quantum Communication, Computing, and Measurement

Abstract

The author studies the relation between the attainable Cramér-Rao type bound and the duality theorem in the infinite dimensional linear programming. By this approach, the attainable Cramér-Rao type bound for a 3-parameter spin 1/2 model is explicitly derived.

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References

  1. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North.Holland, Amsterdam, 1982).

    MATH  Google Scholar 

  2. H. P. Yuen and M. Lax, “Multiple-parameter quantum estimation and measurement of nonselfadjoint observables,” IEEE trans. Inform. Theory, IT-19, pp740–750 (1973).

    Article  MathSciNet  Google Scholar 

  3. H. Nagaoka, “A generalization of the simultaneous diagonalization of hermitian matrices and its relation to quantum estimation theory,” Trans. Jap. Soci. Ind. App. Math., vol.1, No.4, pp.305–318 (1991)(in Japanese).

    Google Scholar 

  4. A. Fujiwara and H. Nagaoka, “Coherency in view of quantum estimation theory,” in Quantum coherence and decoherence, edited by K. Fujikawa and Y. A. Ono, (Elsevier, Amsterdam, 1996), pp.303–306.

    Google Scholar 

  5. R. M. Van Style and R. J. B. Wets, “A duality theory for abstract mathematical programs with applications to optimal control theory,” Journal of mathematical analysis and application, vol.22, pp.679–706,(1968).

    Article  Google Scholar 

  6. A. S. Holevo, “Commutation superoperator of a state and its application to the noncommutative statistics,” Reports on mathematical physics, vol.12, pp.251–271,(1977).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. M. Hayashi, “The minimization of deviation under locally unbiased conditions,” Master’s Thesis, Depertment of Mathematics, Kyoto University,(1996)(in Japanese).

    Google Scholar 

  8. M. Hayashi, “A Linear Programming Approach to Attainable Cramér-Rao type Bounds and Randomness Condition,” to appear.

    Google Scholar 

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© 1997 Springer Science+Business Media New York

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Hayashi, M. (1997). A Linear Programming Approach to Attainable Cramér-Rao Type Bounds. In: Hirota, O., Holevo, A.S., Caves, C.M. (eds) Quantum Communication, Computing, and Measurement. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5923-8_11

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  • DOI: https://doi.org/10.1007/978-1-4615-5923-8_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7716-0

  • Online ISBN: 978-1-4615-5923-8

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