Unextendible maximally entangled bases in dxd

Abstract

We investigate the unextendible maximally entangled bases in ${\mathbb{C}}^d⨂{\mathbb{C}}^d$ and present a $30$-number UMEB construction in ${\mathbb{C}}^6⨂{\mathbb{C}}^6$. For higher dimensional case, we show that for a given $N$-number UMEB in ${\mathbb{C}}^d⨂{\mathbb{C}}^d$, there is a $\tilde{N}$-number, $\tilde{N}=(qd{)}^2-(d^2-N)$, UMEB in ${\mathbb{C}}^{qd}⨂{\mathbb{C}}^{qd}$ for any $q\in \mathbb{N}$. As an example, for ${\mathbb{C}}^{12n}⨂{\mathbb{C}}^{12n}$ systems, we show that there are at least two sets of UMEBs which are not equivalent.

Errors corrected

References in corpus (2)

• Unextendible maximally entangled bases and mutually unbiased bases
• Unextendible maximally entangled bases in ${\mathbb{C}}^d⨂{\mathbb{C}}^{d^{\prime }}$

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• Constructions of Unextendible Maximally Entangled Bases in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\)
• Unextendible product operator basis
• Mutually-orthogonal unitary and orthogonal matrices