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 ⊗ 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 ⊗ C d . And we construct d (d - 1) MUMEBs in bipartite system C d ⊗ C d explicitly. [ABSTRACT FROM AUTHOR]