Exact Bures probabilities that two quantum bits are classically correlated

In previous studies, we have explored the ansatz that the volume elements o f the Bures metrics over quantum systems might serve as prior distributions , in analogy with the (classical) Bayesian role of the volume elements ("Je ffreys' priors") of Fisher information metrics. Continuing this work, we ob tain exact Bures prior probabilities that the members of certain low dimens ional subsets of the fifteen-dimensional convex set of 4 x 4 density matric es are separable or classically correlated. The main analytical tools emplo yed are symbolic integration and a formula of Dittmann (J. Phys. A 32, 2663 (1999)) for Bures metric tensors. This study complements an earlier one (J . Phys. A 32, 5261 (1999)) in which numerical (randomization) - but not int egration - methods were used to estimate Bures separability probabilities f or unrestricted 4 x 4 and 6 x 6 density matrices. The exact values adduced here for pairs of quantum bits (qubits), typically, well exceed the estimat e (approximate to 0.1) there, but this disparity may be attributable to our focus on special low-dimensional subsets. Quite remarkably, for the q =1 a nd q = 1/2 states inferred using the principle of maximum nonadditive (Tsal lis) entropy, the Bures probabilities of separability are both equal to roo t2 - 1. For the Werner qubit-qutrit and qutrit-qutrit states, the probabili ties are vanishingly small, while in the qubit-qubit case it is 1/4.