Related papers: Uniform Probability Distribution Over All Density Matrices

Uniform Probability Distribution Over All Density Matrices

URL: http://arxiv.org/abs/2003.13087v2
Date: Thu, 9 Apr 2020 11:11:07 GMT
Title: Uniform Probability Distribution Over All Density Matrices
Authors: Eddy Keming Chen, Roderich Tumulka
Abstract summary: We identify a probability measure $u$ on $mathscrD$ that can be regarded as the uniform distribution over $mathscrD$. We compute the joint distribution of the eigenvalues of a random density matrix distributed according to this measure.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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