Minimal output entropy for the channels that add or remove a box of a Young diagram, and a Pauli principle for every permutation symmetry
Year: 2026
Type: preprint
Abstract: Two irreducible representations of $U(d)$ whose Young diagrams differ by a single box are connected by four covariant quantum channels: the box can be removed or added, and one keeps either the new diagram or the box ($\mathbb{C}^d$ or its dual). We prove that for each of these channels the output of a coherent state majorizes every other output, so that coherent states minimize the output entropy, and we compute the optimal output explicitly in terms of hook lengths. For the two channels that keep the box we also determine all minimizers; these need not be coherent, even when they are pure. As an application we consider $N$ particles with a given permutation symmetry and find sharp bounds on the spectrum of the reduced density matrix of a single particle, as well as the exact set of spectra that mixed states can reach (for fermions these are the Pauli principle and Coleman's theorem).
Source: arXiv (Cornell University)
Author: Reuvers, Robin
Institution: Roma Tre University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214775918