Bures Measures over the Spaces of Two and Three-Dimensional Density Matrices

Abstract

Due to considerable recent interest in the use of density matrices for a wide variety of purposes, including quantum computation, we present a general method for their parameterizations in terms of Euler angles. We assert that this is of more fundamental importance than (as several people have remarked to us) ``just another parameterization of the density matrix.'' There are several uses to which this methodology can be put. One that has received particular attention is in the construction of certain distinguished (Bures) measures on the $(n^2-1)$-dimensional convex sets of $n\times n$ density matrices.

8 pages, no figures, using LaTeX2e with the Elsevier package

References in corpus (2)

• Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
• Exact Bures Probabilities that Two Quantum Bits are Classically Correlated

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• Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance
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• Numerical Bayesian state assignment for a three-level quantum system. I. Absolute-frequency data; constant and Gaussian-like priors
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• Mixed State Holonomies
• Numerical Bayesian quantum-state assignment for a three-level quantum system. II. Average-value data with a constant, a Gaussian-like, and a Slater prior
• Monotonicity Properties of Certain Measures over the Two-Level Quantum Systems