Constructions of unextendible entangled bases

2019/06/25 by Fei Shi, Xiande Zhang, Shi, Fei +3
Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Quantum Physics (quant-ph) #math.CO #quant-ph

paper · pdf · doi:10.48550/arxiv.1906.10314

13 pages

arxiv created 2019/06/25 · arxiv updated 2019/06/26

Abstract

We provide several constructions of special unextendible entangled bases with fixed Schmidt number k (SUEBk) in ℂ^d⊗ ℂ^d' for 2≤ k≤ d≤ d'. We generalize the space decomposition method in Guo [Phys. Rev. A 94, 052302 (2016)], by proposing a systematic way of constructing new SUEBks in ℂ^d⊗ ℂ^d' for 2≤ k < d ≤ d' or 2≤ k=d< d'. In addition, we give a construction of a (pqdd'-p(dd'-N))-number SUEBpk in ℂ^pd⊗ ℂ^qd' from an N-number SUEBk in ℂ^d⊗ ℂ^d' for p≤ q by using permutation matrices. We also connect a (d(d'-1)+m)-number UMEB in ℂ^d⊗ ℂ^d' with an unextendible partial Hadamard matrix H_{m× d} with m<d, which extends the result in [Quantum Inf. Process. 16(3), 84 (2017)].

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