dorsal/arxiv
View SchemaAll Moments of the Uniform Ensemble of Quantum Density Matrices
| Authors | Robert R. Tucci |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0206193 |
| URL | https://arxiv.org/abs/quant-ph/0206193 |
Abstract
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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"abstract": "Given a uniform ensemble of quantum density matrices $\\rho$, it is useful to\ncalculate the mean value over this ensemble of a product of entries of $\\rho$.\nWe show how to calculate such moments in this paper. The answer involves well\nknown results from Group Representation Theory and Random Matrix Theory. This\nquantum problem has a well known classical counterpart: given a uniform\nensemble of probability distributions $P=(P_1, P_2, ..., P_N)$ where the $P_j$\nare non-negative reals that sum to one, calculate the mean value over this\nprobability simplex of products of $P$ components. The answer to the classical\nproblem follows from an integral formula due to Dirichlet.",
"arxiv_id": "quant-ph/0206193",
"authors": [
"Robert R. Tucci"
],
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"quant-ph"
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"title": "All Moments of the Uniform Ensemble of Quantum Density Matrices",
"url": "https://arxiv.org/abs/quant-ph/0206193"
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