Uniform Probability Distribution Over All Density Matrices

Quantum Studies: Mathematics and Foundations (2022)
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Abstract

Let ℋ be a finite-dimensional complex Hilbert space and D the set of density matrices on ℋ, i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure u on D that can be regarded as the uniform distribution over D. We propose a measure on D, argue that it can be so regarded, discuss its properties, and compute the joint distribution of the eigenvalues of a random density matrix distributed according to this measure.

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Eddy Keming Chen
University of California, San Diego