March 7, 2017

A Hacker's Revenge

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Schack, J. Math. Phys. M. A. Thomas, Elements of Information Theory (Wiley, New York, 1991), p. 231 A. L. Cavalli-Sforza, F. Conterio, Atti. Assoc. Genet. Ital. L. F. Edwards, Am. J. Hum. Genet. 19, 233 (1967) F. W. Tukey, J. Am. Stat. Assoc. 44, 174 (1949) N. Takezaki, M. K. Wootters, Phys. Rev. L. M. Caves, Phys. Rev. Lett. 72, 3439 (1994) P. Goyal, New J. Phys. 12, 023012 (2010) S. Sykora, J. Stat. Phys. 11, 17–27 (1974) G. Zauner, Quantum designs—foundations of a non-commutative theory of designs.

1 A Modal World The world of modal quantum theory is a world without probabilities. Probabilities are so familiar that it is worthwhile to consider more carefully what their absence entails. In a probabilistic world, an event x is assigned a numerical probability p(x) such that 0 ≤ p(x) ≤ 1. The probabilities are normalized, so that p(x) = 1 (1) x where the sum extends over a set of mutually exclusive and exhaustive events. Probabilities are related to statistical frequencies. Suppose we perform N independent trials of an experiment and observe event x to occur Nx times.

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