Mutually unbiased maximally entangled bases in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$

Abstract

We study mutually unbiased maximally entangled bases (MUMEB's) in bipartite system ${\mathbb{C}}^d\otimes {\mathbb{C}}^d(d\ge 3)$. We generalize the method to construct MUMEB's given in [16], by using any commutative ring $R$ with $d$ elements and generic character of $(R,+)$ instead of ${\mathbb{Z}}_d=\mathbb{Z}/d\mathbb{Z}$. Particularly, if $d=p_1^{a_1}{p}_2^{a_2}\dots p_s^{a_s}$ where $p_1,\dots ,p_s$ are distinct primes and $3\le p_1^{a_1}\le \cdots \le p_s^{a_s}$, we present $p_1^{a_1}-1$ MUMEB's in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ by taking $R={\mathbb{F}}_{p_1^{a_1}}\oplus \cdots \oplus {\mathbb{F}}_{p_s^{a_s}}$, direct sum of finite fields (Theorem 3.3).

References in corpus (2)

• Mutually unbiased bases and generalized Bell states
• Quantum Key Distribution Highly Sensitive to Eavesdropping