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arXiv · 1407.4362

Unextendible entangled bases with fixed Schmidt number

Yu Guo·Shengjun Wu
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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 $\mathbb{C}^d\otimes\mathbb{C}^{d'}$ ($2\leq k<d\leq d'$), 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 $d'$ is proposed. Consequently, it is shown that there are at least $k-r$ (here $r=d$ mod $k$, or $r=d'$ mod $k$) sets of UEBk when $d$ or $d'$ is not the multiple of $k$, while there are at least $2(k-1)$ sets of UEBk when both $d$ and $d'$ are the multiples of $k$.

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Yu Guo, Shengjun Wu. 2014-11-05. Unextendible entangled bases with fixed Schmidt number. https://doi.org/10.1103/physreva.90.054303

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