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Abstract: We investigate the Bell inequalities derived from the graph states withviolations detectable even with the presence of noises, which generalizes theidea of error-correcting Bell inequalities Phys. Rev. Lett. 101, 0805012008. Firstly we construct a family of valid Bell inequalities toleratingarbitrary $t$-qubit errors involving $3t+1$ qubits, e.g., 6 qubits suffice totolerate single qubit errors. Secondly we construct also asingle-error-tolerating Bell inequality with a violation that increasesexponentially with the number of qubits. Exhaustive computer search for optimalerror-tolerating Bell inequalities based on graph states on no more than 10qubits shows that our constructions are optimal for single- and double-errortolerance.

Autor: Qing Chen, Sixia Yu, C.H. Oh


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