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- W2522950589 abstract "We report the results of certain integrations of quantum-theoretic interest, relying, in this regard, upon recently developed parameterizations of Boya et al of the n x n density matrices, in terms of squared components of the unit (n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized volume elements of the (minimal monotone) metric for n = 2 and 3, obtaining thereby Bures prior probability distributions over the two- and three-state systems. Then, as an essential first step in extending these results to n > 3, we determine that the normalization (C_{n}) for the marginal prior probability distribution over the (n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known to equal 2/pi.) The constant C_{5} is also found. It too is associated with a remarkably simple decompositon, involving the product of the eight consecutive prime numbers from 2 to 23. We also preliminarily investigate several cases, n > 5, with the use of quasi-Monte Carlo integration. We hope that the various analyses reported will prove useful in deriving a general formula (which evidence suggests will involve the Bernoulli numbers) for the Hall normalization constant for arbitrary n. This would have diverse applications, including quantum inference and universal quantum coding." @default.
- W2522950589 created "2016-09-30" @default.
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- W2522950589 date "1999-04-29" @default.
- W2522950589 modified "2023-09-27" @default.
- W2522950589 title "Bures Probability Distributions for the Two- and Three-State Quantum Systems" @default.
- W2522950589 hasPublicationYear "1999" @default.
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