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Quantum Physics

Title: Spectral density of mixtures of random density matrices for qubits

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.
Comments: 21 pages, LaTex, 6 figures
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)
Cite as: arXiv:1708.02487 [quant-ph]
  (or arXiv:1708.02487v2 [quant-ph] for this version)

Submission history

From: Lin Zhang [view email]
[v1] Tue, 8 Aug 2017 13:45:36 GMT (300kb)
[v2] Sun, 18 Mar 2018 09:18:04 GMT (547kb)