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Nonlocal Variable-Strength Measurements of N Qubits Using GHZ-like Entanglement

The direct measurement of nonlocal properties of entangled quantum systems has been the subject of several recent experimental investigations. Of particular interest is the implementation of nonlocal measurements via indirect measurement schemes, which allow for greater flexibility in the control of the measurement strength. Building on previous results established in the bipartite case, we present a scheme to implement genuine nonlocal measurements of N-qubit systems with variable strength, using GHZ-like entangled qubit meters. This method can be applied to the joint measurement of commuting product observables, enabling us to distinguish between orthogonal nonlocal states, such as Bell states, with minimal disturbance and arbitrary resolution. An explicit relation between the overall measurement strength and the meter entanglement as quantified by the $n$-tangle is derived, opening the door to a new interpretation of the $n$-tangle as a resource for nonlocal measurements.