Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 13 min ago
PreprintarXiv licencearXiv

Beyond Shor's Conjecture: Optimal Quantum Measurements at Fixed Error

  • Jinbo Wang
  • Qihang Wang
  • Pengcheng Hou
  • Kun Chen
Open at sourcePDFDOICite

Abstract

We prove Shor's conjecture: an orthogonal measurement maximizes the information obtainable from any two quantum states in finite dimension. We then show that an error constraint can require three outcomes. For a class of full-rank qubit pairs, the best orthogonal basis switches abruptly as the error penalty increases. Near the switch, three outcomes yield more information at the same error than any orthogonal measurement or random mixture of them. The extra outcome distinguishes confidence levels in one guess; every outcome is used.

Related

  1. A Frame-Spread Lower Bound for Quantum Entropy Estimation under Fixed Rank-One Measurements
    Xinyu Song
    arXivPreprintarXiv licenceFull textStatisticsQuantum physics & quantum informationarXiv
  2. Time-optimal quantum dynamics under fixed-norm generators
    Oskar A. Prośniak, Karol Życzkowski
    arXivPreprintarXiv licenceFull textMathematical physicsQuantum physics & quantum informationarXiv
  3. Optimal Low-Rank Quantum State Tomography with Bounded-Sample Joint Measurements
    Ashwin Nayak, Xingyu Zhou
    arXivPreprintarXiv licenceFull textGeneral mathematicsQuantum physics & quantum informationarXiv
  4. Information Lower Bound for Regime Boundary Estimation — Optimal Precision Limit at the n² Scale and Universal Constant c=1/8 in the Fixed-Breakpoint Model
    Shuiping Tang
    Zenodo (CERN European Organization for Nuclear Research)PreprintLicence not stated7 citedStatisticsOpenAlex
  5. Optimal large sieve for fixed order characters
    Alexandre de Faveri
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{wang2026beyond,
  title = {{Beyond Shor's Conjecture: Optimal Quantum Measurements at Fixed Error}},
  author = {Jinbo Wang and Qihang Wang and Pengcheng Hou and Kun Chen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.27992},
  eprint = {2609.27992},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27992},
}
RIS
TY  - UNPB
TI  - Beyond Shor's Conjecture: Optimal Quantum Measurements at Fixed Error
AU  - Jinbo Wang
AU  - Qihang Wang
AU  - Pengcheng Hou
AU  - Kun Chen
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.27992
UR  - https://arxiv.org/abs/2609.27992
AB  - We prove Shor's conjecture: an orthogonal measurement maximizes the information obtainable from any two quantum states in finite dimension. We then show that an error constraint can require three outcomes. For a class of full-rank qubit pairs, the best orthogonal basis switches abruptly as the error penalty increases. Near the switch, three outcomes yield more information at the same error than any orthogonal measurement or random mixture of them. The extra outcome distinguishes confidence levels in one guess; every outcome is used.
ER  -