Unextendible maximally entangled bases
Sergey Bravyi, John A. Smolin · Physical Review A · 2011
We introduce the notion of the unextendible maximally entangled basis (UMEB), a set of orthonormal maximally entangled states in ${\mathbb{C}}^{d}\ensuremath{\bigotimes}{\mathbb{C}}^{d}$ 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 $d=4$.