Bounds on k-Uniform Quantum States

2023/10/10 by Shi, Fei, Ning, Yu, Zhao, Qi +1 · 1 citation
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2310.06378

Abstract

Do N-partite k-uniform states always exist when k≤ \lfloor(N)/(2)\rfloor-1? In this work, we provide new upper bounds on the parameter k for the existence of k-uniform states in (ℂ^d)^{⊗ N} when d=3,4,5, which extend Rains' bound in 1999 and improve Scott's bound in 2004. Since a k-uniform state in (ℂ^d)^{⊗ N} corresponds to a pure ((N,1,k+1))_d quantum error-correcting codes, we also give new upper bounds on the minimum distance k+1 of pure ((N,1,k+1))_d quantum error-correcting codes. Furthermore, we generalize Scott's bound to heterogeneous systems, and show some non-existence results of absolutely maximally entangled states in ℂ^d₁⊗(ℂ^d₂)^{⊗ 2n}.

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