Mutually unbiased maximally entangled bases from difference matrices

Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct mutually unbiased bases by difference matrices in the theory of combinatorial designs. In particular, we establish q mutually unbiased bases with q - 1 maximally entangled bases and one product basis in C-q circle times C-q for arbitrary prime power q. In addition, we construct maximally entangled bases for dimension of composite numbers of non-prime power, such as five maximally entangled bases in C-12 circle times C-12 and C-21 circle times C-21, which improve the known lower bounds for d = 3m, with (3, m) = 1 in C-d circle times C-d. Furthermore, we construct p + 1 mutually unbiased bases with p maximally entangled bases and one product basis in C-p circle times C-p2 for arbitrary prime number p.

Automated summary

Based on maximally entangled states, this paper explores the constructions of mutually unbiased bases in bipartite quantum systems. A new way to construct mutually unbiased bases using difference matrices in the theory of combinatorial designs is presented. Various constructions of mutually unbiased bases are established, including cases involving prime power q and composite numbers of non-prime power d.