Unextendible entangled bases with fixed Schmidt number

Abstract

The unextendible product basis (UPB) is generalized to the unextendible entangled basis with any arbitrarily given Schmidt number $k$ (UEBk) for any bipartite system ${\mathbb{C}}^d\otimes {\mathbb{C}}^{d^{\prime }}$ ($2\le k<d\le d^{\prime }$), which can also be regarded as a generalization of the unextendible maximally entangled basis (UMEB). A general way of constructing such a basis with arbitrary $d$ and $d^{\prime }$ is proposed. Consequently, it is shown that there are at least $k-r$ (here $r=d$ mod $k$, or $r=d^{\prime }$ mod $k$) sets of UEBk when $d$ or $d^{\prime }$ is not the multiple of $k$, while there are at least $2(k-1)$ sets of UEBk when both $d$ and $d^{\prime }$ are the multiples of $k$.

4 pages, minor revisions

References in corpus (2)

• Entanglement detection
• Unextendible maximally entangled bases in ${\mathbb{C}}^d⨂{\mathbb{C}}^{d^{\prime }}$

Cited by in corpus (3)

• Entangled bases with fixed Schmidt number
• Constructing UMEB from maximally entangled basis
• Constructions of unextendible entangled bases