The Minimum Size of Qubit Unextendible Product Bases

Author Nathaniel Johnston

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Nathaniel Johnston

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Nathaniel Johnston. The Minimum Size of Qubit Unextendible Product Bases. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 93-105, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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.
  • unextendible product basis; quantum entanglement; graph factorization


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