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arXiv · 2003.13087

Uniform Probability Distribution Over All Density Matrices

Eddy Keming Chen·Roderich Tumulka
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Abstract

Let $\mathscr{H}$ be a finite-dimensional complex Hilbert space and $\mathscr{D}$ the set of density matrices on $\mathscr{H}$, i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure $u$ on $\mathscr{D}$ that can be regarded as the uniform distribution over $\mathscr{D}$. We propose a measure on $\mathscr{D}$, 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, Roderich Tumulka. 2020-03-29. Uniform Probability Distribution Over All Density Matrices. https://doi.org/10.1007/s40509-021-00267-5

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