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arXiv · 1708.02487

Spectral density of mixtures of random density matrices for qubits

Lin Zhang·Jiamei Wang·Zhihua Chen
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Abstract

We derive the spectral density of the equiprobable mixture of two random density matrices of a two-level quantum system. We also work out the spectral density of mixture under the so-called quantum addition rule. We use the spectral densities to calculate the average entropy of mixtures of random density matrices, and show that the average entropy of the arithmetic-mean-state of $n$ qubit density matrices randomly chosen from the Hilbert-Schmidt ensemble is never decreasing with the number $n$. We also get the exact value of the average squared fidelity. Some conjectures and open problems related to von Neumann entropy are also proposed.

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Lin Zhang, Jiamei Wang, Zhihua Chen. 2018-03-18. Spectral density of mixtures of random density matrices for qubits. https://doi.org/10.1016/j.physleta.2018.04.018

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