Mutually unbiased maximally entangled bases in ℂ^d⊗ℂ^d

2016/09/09 by Junying Liu, Minghui Yang, Liu, Junying +3
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.1609.02674

arxiv created 2016/09/09 · arxiv updated 2016/09/12

Abstract

We study mutually unbiased maximally entangled bases (MUMEB's) in bipartite system ℂ^d⊗ℂ^d (d ≥ 3). We generalize the method to construct MUMEB's given in [16], by using any commutative ring R with d elements and generic character of (R,+) instead of ℤ_d=ℤ/dℤ. Particularly, if d=p₁^a₁p₂^a₂… p_s^a_s where p₁, …, p_s are distinct primes and 3≤ p₁^a₁≤⋯≤ p_s^a_s, we present p₁^a₁-1 MUMEB's in ℂ^d⊗ℂ^d by taking R=\mathbbF_p1^a1⊕⋯⊕\mathbbF_ps^as, direct sum of finite fields (Theorem 3.3).

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