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PreprintCC BY 4.0arXiv

Sklar's Theorem and Quantum State Reconstruction from All-Context Dependence

  • Yi-Yu Lin
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Abstract

Sklar's theorem separates the marginals of a joint distribution from its dependence structure. We apply this viewpoint to Born statistics generated by local quantum measurements. For non-product two-qubit states, the dependence nuclei over all local binary projective measurement contexts determine the state up to at most a discrete double-spin-flip ambiguity. The corresponding scalar optimization, combined with the quantum total correlation, reproduces global quantum discord.

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Cite

BibTeXRIS
BibTeX
@misc{lin2026sklars,
  title = {{Sklar's Theorem and Quantum State Reconstruction from All-Context Dependence}},
  author = {Yi-Yu Lin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08035},
  eprint = {2609.08035},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08035},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Sklar's Theorem and Quantum State Reconstruction from All-Context Dependence
AU  - Yi-Yu Lin
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.08035
UR  - https://arxiv.org/abs/2609.08035
AB  - Sklar's theorem separates the marginals of a joint distribution from its dependence structure. We apply this viewpoint to Born statistics generated by local quantum measurements. For non-product two-qubit states, the dependence nuclei over all local binary projective measurement contexts determine the state up to at most a discrete double-spin-flip ambiguity. The corresponding scalar optimization, combined with the quantum total correlation, reproduces global quantum discord.
ER  -