We introduce the notion of the unextendible maximally entangled basis (UMEB), a set of orthonormal maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ consisting of fewer than $d^2$ vectors which have no additional maximally entangled vectors orthogonal to all of them. We prove that UMEBs do not exist for $d=2$ and give explicit constructions for a six-member UMEB with $d=3$ and a 12-member UMEB with $d=4$.

• Received 24 August 2010

DOI:https://doi.org/10.1103/PhysRevA.84.042306