Induced random mixed states are symmetric Dirichlet mixtures

Abstract:We establish an exact equivalence in distribution between $D$-dimensional random mixed states induced by partial traces over $K$-dimensional environments and the Mai-Alquier distribution, a mixture of $K$ independent Haar-random pure states weighted by a symmetric Dirichlet distribution. This identification recasts a class of expectation values for induced ensembles into calculations involving Dirichlet moments and low-order Haar averages on a single-system state space. As applications, we recover exact purity moments up to fourth order, derive the mean Hilbert--Schmidt distance between independent induced ensembles with possibly different environment dimensions, and obtain exact average determinants. These results provide a unified and constructive perspective on induced random mixed states and on the evaluation of quantities such as purity moments, overlaps, and determinants.

arXiv:2609.09421 [quant-ph]

(or arXiv:2609.09421v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.09421 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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