Work

Induced random mixed states are symmetric Dirichlet mixtures

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.09421

Authors: Kirby, Brian T., Greenwood, Alexander C. B., Lohani, Sanjaya, Lukens, Joseph M.

Institutions: Tulane University, DEVCOM Army Research Laboratory, United States Army Combat Capabilities Development Command, University of Toronto, Southern Methodist University, Purdue University West Lafayette, Quantum Science Center

Language: English

Topic: Quantum Mechanics and Applications

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, Southern Methodist University, Division of Electrical, Communications and Cyber Systems

Award: Collaborative Research: Sub-Shot-Noise Limited Distributed Quantum Sensing on a Commercial Metro-Scale Quantum Network via Deep-Learning-Aided Noise Suppression

OpenAlex ID: W7212109145

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