Average coherence and its typicality for random mixed quantum states

Abstract

Wishart ensemble is a useful and important random matrix model used in diverse fields. By realizing induced random mixed quantum states as Wishart ensemble with the fixed-trace one, using matrix integral technique we give a fast track to the average coherence for random mixed quantum states induced via partial-tracing of the Haar-distributed bipartite pure states. As a direct consequence of this result, we get a compact formula of the average subentropy of random mixed states. These obtained compact formulae extend our previous work.

v2: 18 pages, minor errors and misprints are corrected, final version, accepted for publication in J. Phys. A; v1: 17 pages, LaTeX, no figures. Any comments are welcome!

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• Skew information-based coherence generating power of quantum channels
• Average skew information-based coherence and its typicality for random quantum states
• Duistermaat-Heckman measure and the mixture of quantum states
• A variant of Horn's problem and derivative principle
• Annealed averages in spin and matrix models
• Average entropy of a subsystem over a global unitary orbit of a mixed bipartite state
• Estimating coherence with respect to general quantum measurements
• Method for Generating Randomly Perturbed Density Operators Subject to Different Sets of Constraints
• Average of uncertainty-product for bounded observables
• Distribution and generation of quantum coherence for Gaussian states in de Sitter space
• A classical interpretation of the Scrooge distribution