# Exact Bures probabilities that two quantum bits are classically correlated

@article{Slater1999ExactBP, title={Exact Bures probabilities that two quantum bits are classically correlated}, author={Paul B. Slater}, journal={The European Physical Journal B - Condensed Matter and Complex Systems}, year={1999}, volume={17}, pages={471-480} }

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 with the (classical) Bayesian role of the volume elements (“Jeffreys' priors”) of Fisher information metrics. Continuing this work, we obtain exact Bures prior probabilities that the members of certain low-dimensional subsets of the fifteen-dimensional convex set of density matrices are separable or classically correlated…

## 29 Citations

### A priori Probability That Two Qubits Are Unentangled

- MathematicsQuantum Inf. Process.
- 2002

Here, making use of a newly-developed (Euler angle) parameterization of the 4 × 4 density matrices of Tilma, Byrd and Sudarshan, the analysis is extended to the complete 15-dimensional convex set (C) of arbitrarily paired qubits and conjecture that this is but an approximation to the exact Bures/SD probability of separability.

### A priori probability that a qubit–qutrit pair is separable

- Physics, Mathematics
- 2002

We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (Slater 2002 Quantum Inf. Process. 1 387), which was concerned…

### Bures and Hilbert–Schmidt 2 × 2 determinantal moments

- Mathematics
- 2012

We seek to gain insight into the nature of the determinantal moments 〈|ρPT|n|ρ|k〉Bures of generic (nine-dimensional) two-rebit and (fifteen-dimensional) two-qubit systems (ρ), PT denoting partial…

### Dyson indices and Hilbert–Schmidt separability functions and probabilities

- Mathematics
- 2007

A confluence of numerical and theoretical results leads us to conjecture that the Hilbert–Schmidt separability probabilities of the 15- and 9-dimensional convex sets of complex and real two-qubit…

### Numerical and exact analyses of Bures and Hilbert-Schmidt separability and PPT probabilities

- MathematicsQuantum Inf. Process.
- 2019

A quasirandom methodology is employed, recently developed by Martin Roberts, to estimate the separability probabilities, with respect to the Bures (minimal monotone/statistical distinguishability) measure, of generic two-qubit and two-rebit states of Hilbert-Schmidt and Bures qubit-qudit positive-partial-transpose (PPT)-probabilities.

### Extended studies of separability functions and probabilities and the relevance of Dyson indices

- Mathematics
- 2008

### Geometric approach to the distribution of quantum states in bipartite physical systems

- Mathematics
- 2014

Any set of pure states living in a given Hilbert space possesses a natural and unique metric—the Haar measure—on the group U(N) of unitary matrices. However, there is no specific measure induced on…

### A concise formula for generalized two-qubit Hilbert–Schmidt separability probabilities

- Mathematics
- 2013

We report major advances in the research program initiated in ‘Moment-based evidence for simple rational-valued Hilbert–Schmidt generic 2 × 2 separability probabilities’ (Slater and Dunkl 2012 J.…

### Advances in delimiting the Hilbert–Schmidt separability probability of real two-qubit systems

- Mathematics
- 2010

We seek to derive the probability—expressed in terms of the Hilbert–Schmidt (Euclidean or flat) metric—that a generic (nine-dimensional) real two-qubit system is separable, by implementing the…

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