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PreprintarXiv licencearXiv

Rényi Multi-entropy for Stabilizer States: A Finite Field Gauss Sum Problem

  • Bartlomiej Czech
  • Yichen Feng
  • Jonathan Harper
  • Xin-Xiang Ju
  • Yang Zhao
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Abstract

Rényi multi-entropy probes multi-partite structure beyond bipartite spectra, but its behavior in general quantum states and the entanglement structure it captures remain poorly understood. We develop a finite field Gauss sum framework for calculating it in stabilizer states. Within this framework, the replica contraction reduces to a quadratic Gauss sum if and only if the state is locally unitarily equivalent to a stabilizer state. We obtain analytic expressions for the Rényi multi-entropy of all tree graph states and large families of loop graph states. In contrast to their flat bipartite Rényi spectra, stabilizer states generically have nonflat Rényi multi-entropy spectra.

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Cite

BibTeXRIS
BibTeX
@misc{czech2026rényi,
  title = {{Rényi Multi-entropy for Stabilizer States: A Finite Field Gauss Sum Problem}},
  author = {Bartlomiej Czech and Yichen Feng and Jonathan Harper and Xin-Xiang Ju and Yang Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26814},
  eprint = {2610.26814},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26814},
}
RIS
TY  - UNPB
TI  - Rényi Multi-entropy for Stabilizer States: A Finite Field Gauss Sum Problem
AU  - Bartlomiej Czech
AU  - Yichen Feng
AU  - Jonathan Harper
AU  - Xin-Xiang Ju
AU  - Yang Zhao
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26814
UR  - https://arxiv.org/abs/2610.26814
AB  - Rényi multi-entropy probes multi-partite structure beyond bipartite spectra, but its behavior in general quantum states and the entanglement structure it captures remain poorly understood. We develop a finite field Gauss sum framework for calculating it in stabilizer states. Within this framework, the replica contraction reduces to a quadratic Gauss sum if and only if the state is locally unitarily equivalent to a stabilizer state. We obtain analytic expressions for the Rényi multi-entropy of all tree graph states and large families of loop graph states. In contrast to their flat bipartite Rényi spectra, stabilizer states generically have nonflat Rényi multi-entropy spectra.
ER  -