A new construction of mutually unbiased maximally entangled bases in Cq ⊗ Cq

This paper is devoted to constructing mutually unbiased maximally entangled bases (MUMEBs) in C-q circle times C-q, where q is a prime power. We prove that M(q, q) >= q(2) - q + 1 when q is even, and M(q, q) >= q(2) - q + 2 when q is odd, where M(q, q) is the maximal size of the sets of MUMEBs in Cq Cq. This highly raises the lower bounds of M(q, q) given in D. Xu, Quant. Inf. Process. 18(7) (2019) 213; D. Xu, Quant. Inf. Process. 19(6) (2020) 175. It should de noted that the method used in the paper is completely different from that in D. Xu, Quant. Inf. Process. 18(7) (2019) 213; D. Xu, Quant. Inf. Process. 19(6) (2020) 175.