Discrimination of Measurement Paths for a Three-Qubit System

A method of discerning measurement paths in quantum mechanics was conceived by Sala Mayato and Muga [Phys. Lett. A 375 (2011) 3167] and applied to a two-qubit system. There are some calculational errors in that paper. We adopt the method to a three-qubit system where we choose two measurement contexts, i. e., {A, B, C, D} and {A', B', C', D}, that constitute three measurement paths, i.e., D, ABC and A' B' C', for measuring the quantum observable D in such a way that D = ABC = A' B' C'. The observables A, B, C, D and A', B', C', D are pairwise commuting, but A, B, C do not commute with A', B', C'. The expectation values of the observables for the final states produced after performing the Luders' measurement allow us to determine the measurement path that has been taken.