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Multiscale Schmidt-Spectrum Bounds for High-Dimensional Entanglement: Geometric Measures and Schmidt-Number Witnesses — arXiv:2609.21209

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.21209
License (as archived): CC0-1.0
Archived: 2026-10-10T02:52:21.992Z
SHA-256 of the archived text: c85cfb47d464285348a055d5b790e1a16ba1796c855f8bfae1083acd37b4861f
Stable URL of this page: https://metraipolis.com/documento/dc_d925effa5ccb

How to cite

Multiscale Schmidt-Spectrum Bounds for High-Dimensional Entanglement: Geometric Measures and Schmidt-Number Witnesses — arXiv:2609.21209 — arXiv (en), https://arxiv.org/abs/2609.21209 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d925effa5ccb (Metraipolis archive dc_d925effa5ccb, sha256 c85cfb47d464285348a055d5b790e1a16ba1796c855f8bfae1083acd37b4861f)

BibTeX

@misc{dcd925effa5ccb,
  title = {Multiscale Schmidt-Spectrum Bounds for High-Dimensional Entanglement: Geometric Measures and Schmidt-Number Witnesses — arXiv:2609.21209},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.21209},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d925effa5ccb; sha256 c85cfb47d464285348a055d5b790e1a16ba1796c855f8bfae1083acd37b4861f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.21209. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

High-dimensional bipartite entanglement depends on how probability is distributed across the Schmidt spectrum, whereas a single reference-state fidelity resolves only one spectral scale. We develop multiscale Schmidt-spectrum bounds that connect geometric measures with quantitative Schmidt-number witnesses. For any partition of a pure-state Schmidt spectrum, several nested Vidal tails determine block masses. We derive the sharp upper boundary of the associated normalized nuclear-norm coordinate and show that equality holds if and only if the spectrum is uniform within each block. Refining the partition gives a monotone hierarchy of tighter bounds whenever the added tail data distinguish unequal block means. We also solve a relaxed weighted multiscale optimization globally: one scalar parameter specifies its unique full-support optimizer and explicit value on the nontrivial branch. Using the established single-tail fidelity--resource curve as a baseline, we obtain exact-fidelity equality refinements, convex-roof lower bounds for mixed states, and quantitative calibrations of Schmidt-number witnesses. A higher-tail relation further bounds convex-roof extended negativity in terms of Vidal tails and identifies the pure-state equality spectra. Leakage-aware and joint-confidence formulations state how these bounds can be used with incomplete data. Multistep tails require block-resolved or independently certified spectral information; they are not determined by one projector expectation.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-21 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.21209 — 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 2026-10-10T02:31:30.421Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-09-21?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).