Unextendible maximally entangled bases

We introduce the notion of the unextendible maximally entangled basis (UMEB), a set of orthonormal maximally entangled states in Cd-Cd consisting of fewer than d2 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. © 2011 American Physical Society.