1999/11/30 by Paul B. Slater · 31 citations
Computer Science · Mathematics · Physics and Astronomy · #Ansatz #Mathematical physics #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Qubit #Qutrit #Statistical Mechanics and Entropy #Statistical physics #math-ph #math.MP #physics.data-an #quant-ph
paper · pdf · doi:10.1007/s100510070126
published in The European Physical Journal B 17(3), 471-480 (Springer Science+Business Media) · Seventeen pages, LaTeX, eleven postscript figures. In this version, subsequent (!) to publication in European Physical Journal B, we correct the (1,1)-entries of the 4 x 4 matrices given in formulas (6) and (7), that is, the numerators should both read v^2 - x^2 - y^2 - z^2, rather than v^2 - x^2 + y^2 + z^2
openalex publication_date 2000/10/01 · arxiv created 2001/01/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In previous studies, we have explored the ansatz that the volume elements of the Bures metrics over quantum systems might serve as prior distributions, in analogy to the (classical) Bayesian role of the volume elements ("Jeffreys' priors") of Fisher information metrics. Continuing this work, we obtain exact Bures probabilities that the members of certain low-dimensional subsets of the fifteen-dimensional convex set of 4 x 4 density matrices are separable or classically correlated. The main analytical tools employed are symbolic integration and a formula of Dittmann (quant-ph/9908044) for Bures metric tensors. This study complements an earlier one (quant-ph/9810026) in which numerical (randomization) --- but not integration --- methods were used to estimate Bures separability probabilities for unrestricted 4 x 4 or 6 x 6 density matrices. The exact values adduced here for pairs of quantum bits (qubits), typically, well exceed the estimate (.1) there, but this disparity may be attributable to our focus on special low-dimensional subsets. Quite remarkably, for the q = 1 and q = 1/2 states inferred using the principle of maximum nonadditive (Tsallis) entropy, the separability probabilities are both equal to 21/2 - 1. For the Werner qubit-qutrit and qutrit-qutrit states, the probabilities are vanishingly small, while in the qubit-qubit case it is 1/4.