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Exact Bures Probabilities that Two Quantum Bits are Classically Correlated  Paul B. Slater
;  Date: 
13 Nov 1999  Journal:  European Physical Journal B, Oct. 2000, vol. 17 (no.3):47180  Subject:  Quantum Physics; Mathematical Physics; Data Analysis, Statistics and Probability  quantph mathph math.MP physics.dataan  Affiliation:  University of California  Abstract:  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 lowdimensional subsets of the fifteendimensional 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 (quantph/9908044) for Bures metric tensors. This study complements an earlier one (quantph/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 lowdimensional 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 2^{1/2}  1. For the Werner qubitqutrit and qutritqutrit states, the probabilities are vanishingly small, while in the qubitqubit case it is 1/4.  Source:  arXiv, quantph/9911058  Services:  Forum  Review  PDF  Favorites 


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