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arXiv · 1302.1604

The Minimum Size of Qubit Unextendible Product Bases

Nathaniel Johnston
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Abstract

We investigate the problem of constructing unextendible product bases in the qubit case - that is, when each local dimension equals 2. The cardinality of the smallest unextendible product basis is known in all qubit cases except when the number of parties is a multiple of 4 greater than 4 itself. We construct small unextendible product bases in all of the remaining open cases, and we use graph theory techniques to produce a computer-assisted proof that our constructions are indeed the smallest possible.

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Nathaniel Johnston. 2013-02-06. The Minimum Size of Qubit Unextendible Product Bases. https://doi.org/10.4230/lipics.tqc.2013.93

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