4 research outputs found
Constructing mutually unbiased bases from unextendible maximally entangled bases
We study mutually unbiased bases (MUBs) in which all the bases are
unextendible maximally entangled ones. We first present a necessary and
sufficient condition of constructing a pair of MUBs in . Based
on this condition, an analytical and necessary condition for constructing MUBs
is given. Moreover we illustrate our approach by some detailed examples in . The results are generalized to and
a concrete example in is given.Comment: 14 page
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 mutually unbiased bases with
maximally entangled bases and one product basis in for arbitrary prime power . In addition, we construct
maximally entangled bases for dimension of composite numbers of non-prime
power, such as five maximally entangled bases in and , which improve the
known lower bounds for , with in . Furthermore, we construct mutually unbiased bases with
maximally entangled bases and one product basis in for arbitrary prime number .Comment: 24 page