Multipartite unextendible entangled basis

The unextendible entangled basis with any arbitrarily given Schmidt number k (UEBk) in C-d1 circle times C-d2 is proposed in Guo and Wu (Phys Rev A 90: 054303, 2014), 1 < k <= min{d(1), d(2)}, which is a set of orthonormal entangled states with Schmidt number k in a d(1) circle times d(2) system consisting of fewer than d(1)d(2) vectors which have no additional entangled vectors with Schmidt number k in the complementary space. In this paper, we extend it to multipartite case, and a general way of constructing (m + 1)-partite UEBk from m-partite UEBk is proposed (m >= 2). Consequently, we show that there are infinitely many UEBks in C-d1 circle times C-d2 circle times...circle times C-dN with any dimensions and any N >= 3.