Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Cheng, Caohan, Chen, Lin
Institution: Beihang University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G7870695329
OpenAlex ID: W7213256531