Measurement-Induced Nonlocality

Abstract

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 × 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.

An easy measure of quantum correlation

“…However, this is not allowed in quantum systems. Based on this idea, Luo and co-workers proposed the measurement-induced disturbance [21] and nonlocality [22,23] to measure the quantum correlation. Another way to measure the quantum correlation of a quantum state is through the "distance" between the quantum state under consideration and the closest classical state with zero quantum correlation, and such kind of measures are usually called geometric measures [24][25][26][27].…”

Competition between quantum correlations in the quantum-memory-assisted entropic uncertainty relation

“…Its negativity means inseparability [17] and gives the lower bound of the one-way distillable entanglement for ρ AB [18]. It quantifies partial quantum information [19] and can be related with quantum correlation measures [12,[20][21][22][23][24].…”

Decoherence dynamics of measurement-induced nonlocality and comparison with geometric discord for two qubit systems

“…There are separable states which have non-zero value of discord, indicating existence of quantumness beyond entanglement. Measurement-induced nonlocality(MIN) as introduced by Luo and Fu [3] is another type of correlation which reveals a type of nonlocality that also exists in composite quantum systems. There are classical states(i.e., states with vanishing discord) with non-zero measurement induced nonlocality [3,4].…”

“…Measurement-induced nonlocality(MIN) as introduced by Luo and Fu [3] is another type of correlation which reveals a type of nonlocality that also exists in composite quantum systems. There are classical states(i.e., states with vanishing discord) with non-zero measurement induced nonlocality [3,4]. Since our classical world is local so existence of non-zero MIN for classical states exhibits a kind of non-classical trait in those states.…”