Constructions of mutually unbiased entangled bases

2019/11/20 by Shi, Fei, Zhang, Xiande, Chen, Lin
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1911.08761

Abstract

We construct two mutually unbiased bases by maximally entangled states (MUMEBs) in ℂ²⊗ ℂ³. This is the first example of MUMEBs in ℂ^d⊗ ℂ^d' when d\nmid d', namely d' is not divisible by d. We show that they cannot be extended to four MUBs in ℂ⁶. We propose a recursive construction of mutually unbiased bases formed by special entangled states with a fixed Schmidt number k (MUSEBks). It shows that min \t₁,t₂\ MUSEBk₁k₂s in ℂ^pd⊗ ℂ^qd' can be constructed from t₁ MUSEBk₁s in ℂ^d⊗ ℂ^d' and t₂ MUSEBk₂s in ℂ^p⊗ ℂ^q for any d,d',p,q. Further, we show that three MUMEBs exist in ℂ^d⊗ ℂ^d' for any d,d' with d| d', and two MUMEBs exist in ℂ^d⊗ ℂ^d' for infinitely many d,d' with d\nmid d'.

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