Relatings turings use of norm (statistics) to eigenvalues


http://terrytao.wordpress.com/2010/01/09/254a-notes-3-the-operator-norm-of-a-random-matrix/

One recalls how in quantum random walks (on the cryptowheel treated as a circle group) the expansion and the mixing time is not dependent on the second eigenvalue (but all of them, which are sumsuned in the operator norm).

Turing uses the correlation of plaintext as his quantum coin, to refine his graph theoric measure of its information (number of quanta).

For the quantum walk on his cycle graph, he can calulate the expectation value of a walk step between 2 nodes of hamming difference of 1.

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