Intrinsic volumes of the quantum state space and mutually unbiased bases
Year: 2025
Type: article
Abstract: This program estimates, via Monte Carlo (MC) simulation, the coefficients of the polynomial describing the volume of the $\varepsilon$-neighborhood of the \emph{complementarity polytope} constructed from $(N+1)$ mutually orthogonal $N$-vertex simplices in $\mathbb{R}^{N^2-1}$. Note that, in our paper, we use $d$ in place of $N$, since it denotes the dimension of the original complex vector space $\mathbb{C}^d$. The main purpose of this program is to confirm our derived analytic formulas (Theorem 2 in the paper https://arxiv.org/abs/2511.11523) to several decimal places, and the code may be useful to other researchers for estimating further intrinsic volumes.
Author: Szilágyi, Zsombor
Institution: Budapest University of Technology and Economics
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7106329041
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