Mutually unbiased special entangled bases with Schmidt number 2 in C3 ⊗ C4k

A way of constructing special entangled basis with fixed Schmidt number 2 (SEB2) in C-3 circle times C-4k (k is an element of z(+), 3 inverted iota k) is proposed, and the conditions mutually unbiased SEB2s (MUSEB2s) satisfy are discussed. In addition, a very easy way of constructing MUSEB2s in C-3 circle times C-4k (k = 2(l)) (is) presented. We first establish the concrete construction of SEB2 and MUSEB2s in C-3 circle times C-4 and C-3 circle times C-8, respectively, and then generalize them into C-3 circle times C-4k (k is an element of z(+), 3 inverted iota k) and display the condition that MUSEB2s satisfy; we also give general form of two MUSEB2s as examples in C-3 circle times C-4k (k = 2(l)).