Mutually Unbiased Property of Special Entangled Bases

We study mutually unbiased bases formed by special entangled basis with fixed Schmidt number 2 (MUSEB2s) in C-3 circle times C-4p(p is an element of Z(+)). Through analyzing the conditions MUSEB2s satisfy, a systematic way of the concrete construction of MUSEB2s in C-3 circle times C-4p is established. A general approach to constructing MUSMEB2s in C-3 circle times C-4p(p is an element of Z(+)) from MUSMEB2s in C-3 circle times C-4 is also presented. Detailed examples in C-3 circle times C-4, C-3 circle times C-8 and C-3 circle times C-12 are given. Especially, by choosing special entangled basis with fixed Schmidt number 2 (SEB2) from [J. Phys. A. Math. Theor. 48245301(2015)], the limitation of 3 inverted iota p in [Quantum Inf. Process. 17:58(2018)] is successfully deleted.

Automated summary

The research focuses on mutually unbiased bases formed by special entangled basis with fixed Schmidt number 2, establishing a systematic way of construction and proposing a general approach from different contexts. Detailed examples in various environments are provided, and limitations from previous studies are successfully eliminated.