2015/10/31 by Daniel McNulty, Bogdan Pammer, Stefan Weigert · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1063/1.4943301
published as J. Math. Phys. 57, 032202 (2016) · 15 pages, identical to published version
arxiv created 2016/03/17 · arxiv updated 2016/03/18
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.