All Moments of the Uniform Ensemble of Quantum Density Matrices

Details All Moments of the Uniform Ensemble of Quantum Density Matrices All Moments of the Uniform Ensemble of Quantum Density Matrices

2002-06-28

arxiv.org/abs/quant-ph/0206193v1

Physics

Quantum Physics

17 pages (files: 1 .tex, 3 .sty)

Scientific paper

Given a uniform ensemble of quantum density matrices $\rho$, it is useful to calculate the mean value over this ensemble of a product of entries of $\rho$. We show how to calculate such moments in this paper. The answer involves well known results from Group Representation Theory and Random Matrix Theory. This quantum problem has a well known classical counterpart: given a uniform ensemble of probability distributions $P=(P_1, P_2, ..., P_N)$ where the $P_j$ are non-negative reals that sum to one, calculate the mean value over this probability simplex of products of $P$ components. The answer to the classical problem follows from an integral formula due to Dirichlet.

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