Entropy-based random quantum states

• URL: http://arxiv.org/abs/2511.01988v1
• Date: Mon, 03 Nov 2025 19:01:19 GMT
• Title: Entropy-based random quantum states
• Authors: Harry J. D. Miller,
• Abstract summary: In quantum information geometry, the curvature of von-Neumann entropy and relative entropy induce a natural metric on the space of mixed quantum states.<n>We present an algorithm for generating entropy-based random density matrices by sampling a class of bipartite pure states.<n>We find that a distinguishing feature of the ensemble is its larger purity and increased volume towards the boundary of full-rank states.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In quantum information geometry, the curvature of von-Neumann entropy and relative entropy induce a natural metric on the space of mixed quantum states. Here we use this information metric to construct a random matrix ensemble for states and investigate its key statistical properties such the eigenvalue density and probability distribution of entropy. We present an algorithm for generating these entropy-based random density matrices by sampling a class of bipartite pure states, thus providing a new recipe for random state generation that differs from the well established Hilbert-Schmidt and Bures-Hall ensemble approaches. We find that a distinguishing feature of the ensemble is its larger purity and increased volume towards the boundary of full-rank states. The entropy-based ensemble can thus be used as a uninformative prior for Bayesian quantum state tomography in high purity regimes, and as a tool for quantifying typical entanglement in finite depth quantum circuits.

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