The Minimum Size of Qubit Unextendible Product Bases


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.


  • Nathaniel Johnston


Cite as:

  • N. Johnston. The minimum size of qubit unextendible product bases. In Proceedings of the 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC), 2013. doi: 10.4230/LIPIcs.TQC.2013.93

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