Uniform Probability Distribution Over All Density Matrices

Abstract

Let $\mathcal{H}$ be a finite-dimensional complex Hilbert space and $\mathcal{D}$ the set of density matrices on $\mathcal{H}$, i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure $u$ on $\mathcal{D}$ that can be regarded as the uniform distribution over $\mathcal{D}$. We propose a measure on $\mathcal{D}$, 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.

9 pages LaTeX, no figures; v2 last paragraph added, references [10,13-16] added

References in corpus (3)

• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
• On the Role of Density Matrices in Bohmian Mechanics
• All Moments of the Uniform Ensemble of Quantum Density Matrices

Cited by in corpus (1)

• From Time Asymmetry to Quantum Entanglement: The Humean Unification