Research ArticleOpen AccessGoogle Scholar indexed
Re-Formulation of Mean King’s Problem Using Shannon’s Entropy
Graduate School of Science and Engineering, Chuo University, Tokyo, Japan
Graduate School of Science and Engineering, Chuo University, Tokyo, Japan
- 1 Graduate School of Science and Engineering, Chuo University, Tokyo, Japan
- 2 Graduate School of Science and Engineering, Chuo University, Tokyo, Japan
Journal of Quantum Information Science·Volume 03 (2013)·Pages 6–9·Published 29 March 2013·DOI10.4236/jqis.2013.31002
Copy link · social · email
Abstract
Mean King’s problem is formulated as a retrodiction problem among noncommutative observables. In this paper, we reformulate Mean King’s problem using Shannon’s entropy as a first step of introducing quantum uncertainty relation with delayed classical information. As a result, we give informational and statistical meanings to the estimation on Mean King problem. As its application, we give an alternative proof of nonexistence of solutions of Mean King’s problem for qubit system without using entanglement.
KeywordsMean King’s ProblemQuantum Retrodiction ProblemQuantum Estimation ProblemShannon’s Entropy
- L. Vaidman, Y. Aharonov and D. Z. Albert, “How to Ascertain the Values of σ x, σ y, and σ z of a Spin-1/2 Particle,” Physical Review Letters, Vol. 58, No. 14, 1987, pp. 1385-1387. doi:10.1103/PhysRevLett.58.1385
- B.-G. Englert and Y. Aharonov, “The Mean King’s Problem: Prime Degrees of Freedom,” Physics Letters A, Vol. 284, No. 1, 2001, pp. 1-5. doi:10.1016/S0375-9601(01)00271-7
- A. Hayashi, M. Horibe and T. Hashimoto, “Mean King’s Problem with Mutually Unbiased Bases and Orthogonal Latin Squares,” Physical Review A, Vol. 71, No 5, 2005, Article ID: 052331. doi:10.1103/PhysRevA.71.052331
- G. Kimura, H. Tanaka and M. Ozawa, “Solution to the Mean King’s Problem with Mutually Unbiased Bases for Arbitrary Levels,” Physical Review A, Vol. 73, No. 5, 2006, Article ID: 050301(R). doi:10.1103/PhysRevA.73.050301
- M. Reimpell and R. F. Werner, “A Meaner King Uses Biased Bases,” Physical Review A, Vol. 75, No. 6, 2007, Article ID: 062334. doi:10.1103/PhysRevA.75.062334
- G. Kimura, H. Tanaka and M. Ozawa, “Comments on “Best Conventional Solutions to the King’s Problem,” Zeitschrift für Naturforschung, Vol. 62a, 2007, pp. 152-156. http://www.znaturforsch.com/aa/v62a/s62a0152.pdf
- P. K. Aravind, “Best Conventional Solutions to the King’s Problem,” Zeitschrift für Naturforschung, Vol. 58a, 2003, pp. 682-690. http://www.znaturforsch.com/aa/v58a/s58a0085.pdf
- I. D. Ivanovic, “Geometrical Description of Quantum State Determination,” Journal of Physics A: Mathematical and General, Vol. 14, No. 12, 1981, pp. 3241-3245. doi:10.1088/0305-4470/14/12/019
- W. K. Wootters and B. D. Fields, “Optimal State-Determination by Mutually Unbiased Measurements,” Annals of Physics, Vol. 191, No. 2, 1988, pp. 363-381. doi:10.1016/0003-4916(89)90322-9
- M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information,” Cambridge University Press, Cambridge, 2000.
- M. Hayashi, “Quantum Information an Introduction,” Springer-Verlag, Berlin and Heidelberg, 2006.