Mutually unbiased special entangled bases with Schmidt number 2d in ℂ2d+1 ⊗ ℂ4d

In this paper, we construct mutually unbiased special entangled bases with Schmidt number 2d in [Formula: see text]. Precisely, we first provide a necessary and sufficient condition for two special entangled bases with Schmidt number 2d are mutually unbiased, and then use the condition to construct two mutually unbiased special entangled bases with Schmidt number 2 in [Formula: see text] and two mutually unbiased special entangled bases with Schmidt number 4 in [Formula: see text].