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Localizable Bipartite Rank-One Ideal Measurements Have a Block-Replicated Nice-Bell Structure — arXiv:2609.22181

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.22181
License (as archived): CC0-1.0
Archived: 2026-10-09T22:46:26.583Z
SHA-256 of the archived text: af77200469a1368fec37452124df9df82ace4817ed9699d65e963fdcb5c7aa17
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How to cite

Localizable Bipartite Rank-One Ideal Measurements Have a Block-Replicated Nice-Bell Structure — arXiv:2609.22181 — arXiv (en), https://arxiv.org/abs/2609.22181 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2cf045cc7ffc (Metraipolis archive dc_2cf045cc7ffc, sha256 af77200469a1368fec37452124df9df82ace4817ed9699d65e963fdcb5c7aa17)

BibTeX

@misc{dc2cf045cc7ffc,
  title = {Localizable Bipartite Rank-One Ideal Measurements Have a Block-Replicated Nice-Bell Structure — arXiv:2609.22181},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.22181},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2cf045cc7ffc; sha256 af77200469a1368fec37452124df9df82ace4817ed9699d65e963fdcb5c7aa17},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.22181. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove a complete structural characterization of finite-dimensional bipartite rank-one ideal projective measurements that are localizable without communication in the sense of Akibue and Miyazaki. Up to local-unitary equivalence, every such measurement basis is obtained by replicating a single nice Bell basis across equal-dimensional local subspace blocks. The necessity proof combines the causal block structure of complete measurements established by Beckman, Gottesman, Nielsen, and Preskill with their eigenstate-composition theorem for localizable superoperators. A reference block is first forced to be a nice Bell basis; the same theorem then propagates that basis consistently along every row, column, and interior block. The converse follows from the explicit localization protocol of Akibue and Miyazaki. This establishes their Conjecture 1 and gives a protocol-independent classification of bipartite rank-one ideal measurements in this setting.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-22 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.22181 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T22:25:52.290Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-09-22?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).