Krawtchouk matrices from classical and quantum random walks

摘要: Krawtchouk's polynomials occur classically as orthogonal with respect to the binomial distribution. They may be also expressed in form of matrices, that emerge arrays values take. The algebraic properties these matrices provide a very interesting and accessible example approach probability theory known quantum probability. First it is noted how Krawtchouk are connected classical symmetric Bernoulli random walk. And we show derive context via tensor powers elementary Hadamard matrix. Then connections situation shown by calculating expectation case.