|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'585
Articles rated: 2609
24 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems | | Paul B. Slater
; | | Date: |
29 Apr 1999 | | Journal: | J.Phys. A32 (1999) 8231-8246 | | Subject: | Quantum Physics; Mathematical Physics | quant-ph math-ph math.MP | | Affiliation: | University of California | | 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 Bures (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 "Hall normalization constant" (C_{n}) for the marginal Bures 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. | | Source: | arXiv, quant-ph/9904101 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER