Systematic construction of multiqubit unextendible product bases

• URL: http://arxiv.org/abs/2609.14788v1
• Date: Sun, 13 Sep 2026 20:55:51 GMT
• Title: Systematic construction of multiqubit unextendible product bases
• Abstract summary: We give a systematic construction of multiqubit unextendible product bases.<n> Row decompositions of small UOMs produce the main intervals.<n>Nonexistence of other UPB sizes follows from counts of fibres and row pairs.
• Score: 4.115763274264731
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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