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PreprintarXiv licencearXiv

Tightness of and counterexamples to several quantum estimates

  • Joseph Slote
  • Alexander Volberg
  • Haonan Zhang
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Abstract

We prove here several tightness results for such quantum inequalities as 1) the comparison of operator norm and product norm of d-local hamiltonians, 2) Bohnenblust--Hille inequality for d-local hamiltonians, 3) for quantum Fourier entropy-influence conjecture. We give a deterministic prove of the sharpness of Bohnenblust--Hille exponent. We also discuss the quantum Aaronson--Ambainis conjecture in a special case of anti-commuting Pauli strings.

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Cite

BibTeXRIS
BibTeX
@misc{slote2026tightness,
  title = {{Tightness of and counterexamples to several quantum estimates}},
  author = {Joseph Slote and Alexander Volberg and Haonan Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.04411},
  eprint = {2608.04411},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.04411},
}
RIS
TY  - UNPB
TI  - Tightness of and counterexamples to several quantum estimates
AU  - Joseph Slote
AU  - Alexander Volberg
AU  - Haonan Zhang
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2608.04411
UR  - https://arxiv.org/abs/2608.04411
AB  - We prove here several tightness results for such quantum inequalities as 1) the comparison of operator norm and product norm of d-local hamiltonians, 2) Bohnenblust--Hille inequality for d-local hamiltonians, 3) for quantum Fourier entropy-influence conjecture. We give a deterministic prove of the sharpness of Bohnenblust--Hille exponent. We also discuss the quantum Aaronson--Ambainis conjecture in a special case of anti-commuting Pauli strings.
ER  -