Abstract
Abstract
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
⊗
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
⊗
C
12
and
C
21
⊗
C
21
, which improve the known lower bounds for d = 3m, with (3, m) = 1 in
C
d
⊗
C
d
. Furthermore, we construct p + 1 mutually unbiased bases with p maximally entangled bases and one product basis in
C
p
⊗
C
p
2
for arbitrary prime number p.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
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