Construction of a Family of Maximally Entangled Bases in <b>ℂ<i>^d</i></b> <b>⊗</b> <b>ℂ<i>^d′</i></b>

Abstract

In this paper, we present a new method for the construction of maximally entangled states in Cd⊗Cd′ when d′≥2d. A systematic way of constructing a set of maximally entangled bases (MEBs) in Cd⊗Cd′ was established. Both cases when d′ is divisible by d and not divisible by d are discussed. We give two examples of maximally entangled bases in C2⊗C4, which are mutually unbiased bases. Finally, we found a new example of an unextendible maximally entangled basis (UMEB) in C2⊗C5.

Keywords

• maximally entangled states
• mutually unbiased bases
• unextendible maximally entangled basis