We interpret the maximum global effect caused by locally invariant measurements as measurement-induced nonlocality, which is in some sense dual to the geometric measure of quantum discord [Dakic, Vedral, and Brukner, Phys. Rev. Lett. 105, 190502 (2010)]. We quantify measurement-induced nonlocality from a geometric perspective in terms of measurements, and obtain analytical formulas for any dimensional pure states and $2\times n$ dimensional mixed states. We further derive a tight upper bound to measurement-induced nonlocality in general case. The physical significance of measurement-induced nonlocality is discussed in the context of correlations, entanglement, quantumness, and cryptographic communication.

• Received 8 November 2010

DOI:https://doi.org/10.1103/PhysRevLett.106.120401