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On the Impossibility to Extend Triples of Mutually Unbiased Product Bases in Dimension Six

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Publication details

JournalINTERNATIONAL JOURNAL OF QUANTUM INFORMATION
DatePublished - 11 Sep 2012
Issue number5
Volume10
Number of pages12
Original languageEnglish

Abstract

An analytic proof is given which shows that it is impossible to extend any triple of mutually unbiased (MU) product bases in dimension six by a single MU vector. Furthermore, the 16 states obtained by removing two orthogonal states from any MU product triple cannot figure in a (hypothetical) complete set of seven MU bases. These results follow from exploiting the structure of MU product bases in a novel fashion, and they are among the strongest ones obtained for MU bases in dimension six without recourse to computer algebra.

    Research areas

  • Quantum Physics (quant-ph), Mutually unbiased bases; , complementarity; , finite-dimensional quantum systems

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