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**20160113MUProductBasesForMultipleQudits(resubmitted)**163 KB, PDF-document

Journal | Journal of Mathematical Physics |
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Date | E-pub ahead of print - 14 Mar 2016 |

Date | Published (current) - Mar 2016 |

Issue number | 3 |

Volume | 57 |

Number of pages | 12 |

Early online date | 14/03/16 |

Original language | English |

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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