Spectral density of two kinds of mixtures of random density matrices for qubits
Year: 2017
Type: preprint
Abstract: Investigation about various random quantum state ensembles is always focused on its eigenvalue statistics. Analytical derivation of joint probability distribution density functions of quantum state ensembles can be used to study asymptotical phenomenon and concentration of measure phenomenon in high dimensions. In this paper, however, we will derive the spectral density of equiprobable mixture of two random density matrices for qubits. Besides, we will also work out the spectral density of mixture under the so-called quantum addition rule (see details in the text), proposed in this http URL (J.Math.Phys. 57, 052202 (2016)] of two random density matrices for qubits. We also introduce a new divergence by mimicking the quantum Jensen-Shannon divergence. Unfortunately, our numerical experiments show that both the divergence and its square root are not valid metric.
Source: arXiv (Cornell University)
Authors: Lin Zhang, Jiamei Wang, Zhihua Chen
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2743672929