Mutually unbiased bases as extremal probes of isotropic random Hamiltonians
Abstract
Mutually unbiased bases (MUBs) are central finite structures in quantum information. We ask whether complete MUB systems have an extremal probing property beyond their projective 2-design identities. For an isotropic Gaussian traceless Hamiltonian, we prove that, among labeled unions of d+1 orthonormal bases, a complete MUB union has the stochastically largest sampled maximum. Each basis induces the same regular-simplex Gaussian block; mutual unbiasedness eliminates cross-block covariance, joint Gaussianity yields independence, and a centered-convex Gaussian correlation inequality makes this independent coupling extremal. We also derive a radial-mixture extension and prove exact MUB-family collapse for fully matched diagonal-cost constructions.
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BibTeX
@misc{semre2026mutually,
title = {{Mutually unbiased bases as extremal probes of isotropic random Hamiltonians}},
author = {Emilio Semre and Steven Frankel},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.16060},
eprint = {2605.16060},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.16060},
}
RIS
TY - UNPB
TI - Mutually unbiased bases as extremal probes of isotropic random Hamiltonians
AU - Emilio Semre
AU - Steven Frankel
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2605.16060
UR - https://arxiv.org/abs/2605.16060
AB - Mutually unbiased bases (MUBs) are central finite structures in quantum information. We ask whether complete MUB systems have an extremal probing property beyond their projective 2-design identities. For an isotropic Gaussian traceless Hamiltonian, we prove that, among labeled unions of d+1 orthonormal bases, a complete MUB union has the stochastically largest sampled maximum. Each basis induces the same regular-simplex Gaussian block; mutual unbiasedness eliminates cross-block covariance, joint Gaussianity yields independence, and a centered-convex Gaussian correlation inequality makes this independent coupling extremal. We also derive a radial-mixture extension and prove exact MUB-family collapse for fully matched diagonal-cost constructions.
ER -