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.
 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
 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
 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