Unextendible maximally entangled bases in ℂ^d ⊗ ℂ^d

Yan-Ling Wang, Mao-Sheng Li, and Shao-Ming Fei

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Submission date: 01. Oct. 2014
Pages: 6
published in: Physical review / A, 90 (2014) 3, art-no. 034301 
DOI number (of the published article): 10.1103/PhysRevA.90.034301
Bibtex
PACS-Numbers: 03.67.Mn, 03.65.Ud, 03.67.Hk
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Abstract:
We investigate the unextendible maximally entangled bases in ℂ^d ⊗ ℂ^d and present a 30-number UMEB construction in ℂ⁶ ⊗ ℂ⁶. For higher dimensional case, we show that for a given N-number UMEB in ℂ^d ⊗ ℂ^d, there is a -number, = (qd)² − (d² − N), UMEB in ℂ^qd ⊗ ℂ^qd for any q ∈ ℕ. As an example, for ℂ¹²ⁿ ⊗ ℂ¹²ⁿ systems, we show that there are at least two sets of UMEBs which are not equivalent.