Mutually unbiased maximally entangled bases in Cd ⊗ Cd with d an odd prime power

We study mutually unbiased maximally entangled bases (MUMEBs) in bipartite system C-d circle times C-d with d >= 3 a power of an odd prime number. By using the theory of finite fields, we provide a new and intuitive method to construct MUMEBs in C-d circle times C-d. And we construct d(d - 1) MUMEBs in bipartite system C-d circle times C-d explicitly.

Automated summary

We study mutually unbiased maximally entangled bases (MUMEBs) in bipartite system C-d⨂C-d with d >= 3, where d is a power of an odd prime number. By utilizing the theory of finite fields, we present a novel and intuitive method for constructing MUMEBs in C-d⨂C-d. Specifically, we construct d(d - 1) MUMEBs in the bipartite system C-d⨂C-d explicitly.