2019/09/22 by Yan-Ling Wang, Wang, Yan-Ling
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1909.10043
8 pages, 4 figures
arxiv created 2019/09/22 · openalex publication_date 2019/09/22 · arxiv updated 2019/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Special unextendible entangled basis of "type k" (SUEBk), a set of incomplete orthonormal special entangled states of "type k" whose complementary space has no special entangled state of "type k". This concept can be seem as a generalization of the unextendible product basis (UPB) introduced by Bennett et al. in [ Phys. Rev. Lett. 82, 5385(1999) ] and the unextendible maximally entangled basis (UMEB) introduced by Bravyi and Smolin in [Phys. Rev. A 84, 042306(2011)]. We present an efficient method to construct sets of SUEBk. The main strategy here is to decompose the whole space into two subspaces such that the rank of one subspace can be easily upper bounded by k while the other one can be generated by two kinds of the special entangled states of type k. This method is very effective for those k=pm≥ 3 where p is a prime number. For these cases, we can otain sets of SUEBk with continuous integer cardinality when the local dimensions are large. Moreover, one can find that our method here can be easily extended when there are more than two kinds of the special entangled states of type k at hand.