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Open Quantum Systems Decoherence Quantum Simulation

Summing free unitary random matrices

arXiv

Authors: Andrzej Jarosz

Year

2010

Paper ID

10696

Status

Preprint

Abstract Read

~2 min

Abstract Words

108

Citations

N/A

Abstract

I use quaternion free probability calculus - an extension of free probability to non-Hermitian matrices (which is introduced in a succinct but self-contained way) - to derive in the large-size limit the mean densities of the eigenvalues and singular values of sums of independent unitary random matrices, weighted by complex numbers. In the case of CUE summands, I write them in terms of two "master equations," which I then solve and numerically test in four specific cases. I conjecture a finite-size extension of these results, exploiting the complementary error function. I prove a central limit theorem, and its first sub-leading correction, for independent identically-distributed zero-drift unitary random matrices.

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This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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I use quaternion free probability calculus - an extension of free probability to non-Hermitian matrices (which is introduced in a succinct but self-contained way) - to derive...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1010.5220 [2] arXiv https://arxiv.org/abs/1010.5220 [3] Publisher https://arxiv.org/abs/1010.5220

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