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PreprintarXiv licencearXiv

Systematic construction of multiqubit unextendible product bases

  • Caohan Cheng
  • Lin Chen
Open at sourcePDFDOICite

Abstract

The construction of multiqubit unextendible product bases (UPBs) has been a long-standing problem. We give a systematic construction of multiqubit UPBs by studying their unextendible orthogonal matrices (UOMs) with graph-theoretic methods. Row decompositions of small UOMs produce the main intervals. Com- pletion graphs settle the remaining small UPB sizes, except for one size obtained from a good column structure. Nonexistence of the other UPB sizes follows from counts of fibres and row pairs. The computer is used only for a few finite UOM checks, whose exact tests are stated in the certificate appendix. These arguments determine the complete multiqubit UPB size spectrum in every dimension.

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Cite

BibTeXRIS
BibTeX
@misc{cheng2026systematic,
  title = {{Systematic construction of multiqubit unextendible product bases}},
  author = {Caohan Cheng and Lin Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14788},
  eprint = {2609.14788},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14788},
}
RIS
TY  - UNPB
TI  - Systematic construction of multiqubit unextendible product bases
AU  - Caohan Cheng
AU  - Lin Chen
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14788
UR  - https://arxiv.org/abs/2609.14788
AB  - The construction of multiqubit unextendible product bases (UPBs) has been a long-standing problem. We give a systematic construction of multiqubit UPBs by studying their unextendible orthogonal matrices (UOMs) with graph-theoretic methods. Row decompositions of small UOMs produce the main intervals. Com- pletion graphs settle the remaining small UPB sizes, except for one size obtained from a good column structure. Nonexistence of the other UPB sizes follows from counts of fibres and row pairs. The computer is used only for a few finite UOM checks, whose exact tests are stated in the certificate appendix. These arguments determine the complete multiqubit UPB size spectrum in every dimension.
ER  -