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PreprintCC BY 4.0arXiv

Quantum Tsallis Entropy Estimation: Near-Optimal Bounds and High-Precision Improvements

  • Chengshen Gao
  • Zongxing Xiong
  • Lvzhou Li
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Abstract

Estimating statistical properties of probability distributions is a fundamental problem in statistics and theoretical computer science. We develop quantum algorithms for estimating the q-Tsallis entropy HqTsa(P) =(∑i=1n piq−1)/(1−q) when 0<q<1, given purified quantum query access to a distribution P on [n]. When 0<q≤ 1/2, we provide a quantum algorithm with query complexity Õrbra(n/ε)1/2q, which is optimal up to polylogarithmic factors. When 1/2<q<1, we introduce a two-stage simultaneous probability estimation procedure, yielding a quantum algorithm with query complexity Õ((n1/2+1/2q)/ε1/2q+(n1−q)/ε), which improves the result given by Chen et al. (ICALP 2026) when ε=Orbran1−2q.

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Cite

BibTeXRIS
BibTeX
@misc{gao2026quantum,
  title = {{Quantum Tsallis Entropy Estimation: Near-Optimal Bounds and High-Precision Improvements}},
  author = {Chengshen Gao and Zongxing Xiong and Lvzhou Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22983},
  eprint = {2610.22983},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22983},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quantum Tsallis Entropy Estimation: Near-Optimal Bounds and High-Precision Improvements
AU  - Chengshen Gao
AU  - Zongxing Xiong
AU  - Lvzhou Li
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.22983
UR  - https://arxiv.org/abs/2610.22983
AB  - Estimating statistical properties of probability distributions is a fundamental problem in statistics and theoretical computer science. We develop quantum algorithms for estimating the q-Tsallis entropy H_q^Tsa(P) =(∑_i=1^n p_i^q−1)/(1−q) when 0<q<1, given purified quantum query access to a distribution P on [n]. When 0<q≤ 1/2, we provide a quantum algorithm with query complexity Õrbra(n/ε)^1/2q, which is optimal up to polylogarithmic factors. When 1/2<q<1, we introduce a two-stage simultaneous probability estimation procedure, yielding a quantum algorithm with query complexity Õ((n^1/2+1/2q)/ε^1/2q+(n^1−q)/ε), which improves the result given by Chen et al. (ICALP 2026) when ε=Orbran^1−2q.
ER  -