Spectral density of mixtures of random density matrices for qubits

2017/08/31 by Lin Zhang, Jiamei Wang, Zhihua Chen
Computer Science · Mathematics · Physics and Astronomy · #Physics #Quantum #Quantum Information and Cryptography #Quantum mechanics #Quantum optics and atomic interactions #Qubit #Random Matrices and Applications #Spectral density #Statistical physics #Statistics #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1016/j.physleta.2018.04.018

published as Physics Letters A 382 (23), 1516-1523 (2018) · 21 pages, LaTex, 6 figures

arxiv created 2018/03/18 · openalex publication_date 2018/04/09 · arxiv updated 2018/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Average fidelity between random quantum states
• Average entropy of a subsystem
• Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states
• Polarized ensembles of random pure states
• Properties of classical and quantum Jensen-Shannon divergence
• On the Distribution of the Roots of Certain Symmetric Matrices
• Partial transposition of random states and non-centered semicircular distributions