From Permutation Symmetry to Communication Bounds and Additivity

Abstract

Correlations across channel uses can improve quantum communication rates, making optimization over arbitrarily large blocks a central difficulty in determining quantum capacity. We show how full permutation invariance limits this advantage for every finite-dimensional memoryless channel. The optimized coherent information per use converges to the single-use maximum and consequently attains its supremum at a finite block length. Thus finite-block superadditivity remains possible, while the asymptotic optimization reduces to a single channel use. We also establish a strong converse for pure-source entanglement generation with permutation-invariant inputs: at any fixed rate above the single-use coherent-information maximum, the fidelity tends to zero. Beyond these communication bounds, we identify a common structure underlying completely bounded norms and the sandwiched Rényi channel quantities governing discrimination against a replacer and entanglement-assisted communication. De Finetti reduction and permutation covariance yield systematic alternative proofs of their known multiplicativity and additivity results within a shared variational framework. We further show that, for permutation-invariant inputs, correlations cannot sustain an asymptotic reduction in output entropy per use below the single-use minimum. This entropy limit holds for Rényi orders greater than one and for the von Neumann entropy, extending the role of symmetry from communication bounds to the control of output entropy.

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BibTeX RIS

BibTeX

@misc{khanian2026from,
  title = {{From Permutation Symmetry to Communication Bounds and Additivity}},
  author = {Zahra Baghali Khanian and Debbie Leung and Graeme Smith},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02176},
  eprint = {2610.02176},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02176},
}

RIS

TY  - UNPB
TI  - From Permutation Symmetry to Communication Bounds and Additivity
AU  - Zahra Baghali Khanian
AU  - Debbie Leung
AU  - Graeme Smith
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02176
UR  - https://arxiv.org/abs/2610.02176
AB  - Correlations across channel uses can improve quantum communication rates, making optimization over arbitrarily large blocks a central difficulty in determining quantum capacity. We show how full permutation invariance limits this advantage for every finite-dimensional memoryless channel. The optimized coherent information per use converges to the single-use maximum and consequently attains its supremum at a finite block length. Thus finite-block superadditivity remains possible, while the asymptotic optimization reduces to a single channel use. We also establish a strong converse for pure-source entanglement generation with permutation-invariant inputs: at any fixed rate above the single-use coherent-information maximum, the fidelity tends to zero. Beyond these communication bounds, we identify a common structure underlying completely bounded norms and the sandwiched Rényi channel quantities governing discrimination against a replacer and entanglement-assisted communication. De Finetti reduction and permutation covariance yield systematic alternative proofs of their known multiplicativity and additivity results within a shared variational framework. We further show that, for permutation-invariant inputs, correlations cannot sustain an asymptotic reduction in output entropy per use below the single-use minimum. This entropy limit holds for Rényi orders greater than one and for the von Neumann entropy, extending the role of symmetry from communication bounds to the control of output entropy.
ER  -

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