Systematic construction of multiqubit unextendible product bases

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.

arXiv:2609.14788 [quant-ph]

(or arXiv:2609.14788v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.14788 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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