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Minimal output entropy for the channels that add or remove a box of a Young diagram, and a Pauli principle for every permutation symmetry

  • Robin Reuvers
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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 (ℂd 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).

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Cite

BibTeXRIS
BibTeX
@misc{reuvers2026minimal,
  title = {{Minimal output entropy for the channels that add or remove a box of a Young diagram, and a Pauli principle for every permutation symmetry}},
  author = {Robin Reuvers},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.33498},
  eprint = {2609.33498},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33498},
}
RIS
TY  - UNPB
TI  - Minimal output entropy for the channels that add or remove a box of a Young diagram, and a Pauli principle for every permutation symmetry
AU  - Robin Reuvers
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.33498
UR  - https://arxiv.org/abs/2609.33498
AB  - 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 (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).
ER  -