Maximum-Entropy Ensemble of Quantum Subsystems with a Fixed Average State
Abstract
The reduced density matrices of Haar-random bipartite states form a fixed-trace version of the Wishart ensemble of random matrices, with an asymptotic eigenvalue density given by the Marchenko--Pastur (MP) law. We establish a similar universal form for the maximum-entropy distribution of mixed states subject to a fixed ensemble average, arguing that its eigenvalue density converges asymptotically to that of the correlated Wishart ensemble (CWE). The density is thus obtained by a free multiplicative convolution formula, which we apply to the transverse-field Ising model (TFIM) with a thermal average state to derive a high-temperature leading-order correction to the MP law. We then consider measurement by a random POVM on the purification of the mixed reference state. We show that the resulting mixed-state ensemble is asymptotically equivalent to the CWE, and provide confirming numerical evidence. We return to the TFIM example to compute the entanglement of the system with the ancilla after measurement, and give finite-temperature Page curves for the average entanglement entropies.
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BibTeX
@misc{shakeshaft2026maximumentropy,
title = {{Maximum-Entropy Ensemble of Quantum Subsystems with a Fixed Average State}},
author = {Charlie Shakeshaft and Christopher David White and Harry J. D. Miller},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39712},
eprint = {2610.39712},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39712},
}
RIS
TY - UNPB
TI - Maximum-Entropy Ensemble of Quantum Subsystems with a Fixed Average State
AU - Charlie Shakeshaft
AU - Christopher David White
AU - Harry J. D. Miller
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39712
UR - https://arxiv.org/abs/2610.39712
AB - The reduced density matrices of Haar-random bipartite states form a fixed-trace version of the Wishart ensemble of random matrices, with an asymptotic eigenvalue density given by the Marchenko--Pastur (MP) law. We establish a similar universal form for the maximum-entropy distribution of mixed states subject to a fixed ensemble average, arguing that its eigenvalue density converges asymptotically to that of the correlated Wishart ensemble (CWE). The density is thus obtained by a free multiplicative convolution formula, which we apply to the transverse-field Ising model (TFIM) with a thermal average state to derive a high-temperature leading-order correction to the MP law. We then consider measurement by a random POVM on the purification of the mixed reference state. We show that the resulting mixed-state ensemble is asymptotically equivalent to the CWE, and provide confirming numerical evidence. We return to the TFIM example to compute the entanglement of the system with the ancilla after measurement, and give finite-temperature Page curves for the average entanglement entropies.
ER -