Comment on “Quantum Correlation without Classical Correlations”

摘要

Recently, Kaszlikowski et al. [1] showed that, for oddnn >=3, the n-qubit state u000112...n ¼ 1n2 ðjWihWjþj u0001 Wih u0001 WjÞ,nwhere jWi¼ 1 ffiffinnnp ðj00...01iþj00...10iþu0002u0002u0002þj10...00iÞ,nand j u0001 Wi¼ 1 ffiffinnnp ðj11...10iþj11...01iþu0002u0002u0002þj01...11iÞ,nhas genuine n-partite quantum correlations, and more-nover all n-party covariances CovðX1; ... ;XnÞ¼nhðX1 u0003hX1iÞ u0004 u0002 u0002 u0002 u0004 ðXn u0003hXniÞi of traceless observablesnX1; ... ;Xn vanish for this state. According to the authors ofnRef. [1], if for some choices of local observablesnX1; ... ;Xn the n-party covariance CovðX1; ... ;XnÞ is non-nzero, then an n-qubit state has genuine n-party classicalncorrelations. Moreover, if for all choices of local observ-nables X1; ... ;Xn the n-party covariance CovðX1; ... ;XnÞ isnzero, then an n-qubit state has no genuine n-party classicalncorrelations. Using the latter claim as a criterion of non-nexistence of genuine n-party classical correlations in annn-qubit state, they came to incorrect conclusion that thenstate u000112...n has no genuine n-partite classical correlations.nThe aim of this Comment is to show explicitly that the statenu000112...n does have genuine n-party classical correlationsndespite vanishing of all n-party covariances.