Constructions of unextendible entangled bases

摘要

We provide several constructions of special unextendible entangled bases with fixed Schmidt number k (SUEBk) in C-d. C-d for 2 = k = d = d . We generalize the space decomposition method in Guo (Phys Rev A 94: 052302, 2016), by proposing a systematic way of constructing new SUEBks in Cd. Cd for 2 = k < d = d or 2 = k = d < d . In addition, we give a construction of a (pqdd-p(dd-N))number SUEBpk in Cpd. Cqd from an N-number SUEBk in Cd. Cd for p = q by using permutation matrices. We also connect a (d(d-1)+ m)-number UMEB in Cd. Cd with an unextendible partial Hadamard matrix Hmxd with m < d, which extends the result in Wang et al. (Quantum Inf Process 16: 84, 2017).