Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Semre, Emilio, Frankel, Steven
Institution: Technion – Israel Institute of Technology
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161556833