Mutually Unbiased Product Bases for Multiple Qudits

TY - JOUR

T1 - Mutually Unbiased Product Bases for Multiple Qudits

AU - McNulty, Daniel

AU - Pammer, Bogdan

AU - Weigert, Stefan

N1 - © 2016 AIP Publishing LLC This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

PY - 2016/3

Y1 - 2016/3

N2 - 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.

AB - 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.

U2 - 10.1063/1.4943301

DO - 10.1063/1.4943301

M3 - Article

SN - 0022-2488

VL - 57

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 3

M1 - 032202

ER -