Family of Zeilinger-Horne-Greenberger "W" states lead to stronger nonclassicality than family of Greenberger-Horne-Zeilinger "GHZ" states

Abstract

The N-qubit states of the W class, for N>10, lead to more robust (against noise admixture) violations of local realism, than the GHZ states. These violations are most pronounced for correlations for a pair of qubits, conditioned on specific measurement results for the remaining (N-2) qubits. The considerations provide us with a qualitative difference between the W state and GHZ state in the situation when they are separately sent via depolarizing channels. For sufficiently high amount of noise in the depolarizing channel, the GHZ states cannot produce a distillable state between two qubits, whereas the W states can still produce a distillable state in a similar situation.

v3: 7 pages, 2 figures, REVTeX4; v2: result on comparative yield of singlets added, 1 new figure