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12: 567-594 (1964). [18] R. S. Ingarden. , 9: 273-282 (1965). [19] K. Urbanik. On the concept of information, Bull. Acad. Polon. , S´er. math. astr. , 20: 887-890 (1972). 38 [20] P. W. Shor. Algorithms for quantum computation: discrete logarithms and factoring. In Proceedings, 35 th Annual Symposium on Fundamentals of Computer Science, IEEE Press, Los Alamitos, CA (1994). [21] P. W. Shor. Polynomial time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J.

Since δ can be chosen arbitrarily small, R can be chosen to be as close to H (Y : X) as desired. Now getting the maximum over the prior probabilities of the strings Shannon’s result is found. Shannon’s noisy channel coding theorem: For a noisy channel N the capacity is given by C (N ) = max H (Y : X) , p(x) where the maximum is taken over all input distributions p (x) (a priori distributions) for X, for one use of the channel, and Y is the corresponding induced random variable at the output of the channel.

Smolin. Experimental Quantum Cryptography. J. Cryptology, 5: 3-28 (1992). [34] D. S. Bethune and W. P. Risk. An autocompensating quantum key distribution system using polarization splitting of light. In IQEC’98 Digest of Postdeadline Papers, pages QPD12-2, Optical Society of America, Washington, DC (1998). [35] Donald S. Bethune and William P. Risk. An autocompensating fiber-optic quantum cryptography system based on polarization splitting of light. J. Quantum Electronics, 36(3): 100 (2000). [36] A.