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PreprintarXiv licencearXiv

A Quantum Method of Types

  • Arick Grootveld
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Abstract

The method of types is a fundamental tool in classical information theory, with applications ranging from composite hypothesis testing and universal source coding to the capacity of arbitrarily varying channels. In this work we introduce an empirical operator acting as a quantum analog of the empirical distribution. We show that this empirical operator satisfies combinatorial and large-deviation bounds, which in combination describe a quantum method of types. As an application, we use our method to prove a universal achievability result for composite quantum hypothesis testing.

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Cite

BibTeXRIS
BibTeX
@misc{grootveld2026quantum,
  title = {{A Quantum Method of Types}},
  author = {Arick Grootveld},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.27442},
  eprint = {2606.27442},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.27442},
}
RIS
TY  - UNPB
TI  - A Quantum Method of Types
AU  - Arick Grootveld
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2606.27442
UR  - https://arxiv.org/abs/2606.27442
AB  - The method of types is a fundamental tool in classical information theory, with applications ranging from composite hypothesis testing and universal source coding to the capacity of arbitrarily varying channels. In this work we introduce an empirical operator acting as a quantum analog of the empirical distribution. We show that this empirical operator satisfies combinatorial and large-deviation bounds, which in combination describe a quantum method of types. As an application, we use our method to prove a universal achievability result for composite quantum hypothesis testing.
ER  -