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Mutually Unbiased Product Bases for Multiple Qudits

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Publication details

JournalJournal of Mathematical Physics
DateE-pub ahead of print - 14 Mar 2016
DatePublished (current) - Mar 2016
Issue number3
Number of pages12
Early online date14/03/16
Original languageEnglish


We investigate the interplay between mutual unbiasedness and product bases for multiple qudits of possibly different dimensions. A product state of such a system is shown to be mutually unbiased to a product basis only if each of its factors is mutually unbiased to all the states which occur in the corresponding factors of the product basis. This result implies both a tight limit on the number of mutually unbiased product bases which the system can support and a complete classification of mutually unbiased product bases for multiple qubits or qutrits. In addition, only maximally entangled states can be mutually unbiased to a maximal set of mutually unbiased product bases.

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