We generalize the concept of measurement-induced non-locality (MIN) to an n-partite quantum state. We get exact analytical expressions for MIN in an n-partite pure and n-qubit mixed state. We obtain the conditions under which MiN equals geometric quantum discord in an n-partite pure state and an n-qubit mixed state.
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.
Measurement-induced nonlocality (MIN), introduced by Luo and Fu [Phys. Rev. Lett.106, 120401 (2011)], is a kind of quantum correlation which is different from entanglement and quantum discord (QD). MIN is defined over one-sided projective measurements. In this paper, we introduce a MIN over two-sided projective measurements. The nullity of this two-sided MIN is characterized, a formula for calculating two-sided MIN for pure states is proposed, and a lower bound of (two-sided) MIN for maximally entangled mixed states is given. In addition, we find that (two-sided) MIN is not continuous. Both finite- and infinite-dimensional cases are considered.
Abstract Measurement-induced nonlocality (MIN), a quantum correlation measure for bipartite systems, is an indicator of maximal global effects due to locally invariant von Neumann projective measurements. It is originally defined as the maximal square of the Hilbert–Schmidt norm of the difference between pre- and post-measurement states. In this article, we propose a new form of MIN based on affinity. This quantity satisfies all the criteria of a bona fide measure of quantum correlation measures. This quantity is evaluated for both arbitrary pure and 2 × n dimensional (qubit–qudit) mixed states. The operational meaning of the proposed quantity is interpreted in terms of the interferometric power of the quantum state. We apply these results on two-qubit mixed states, such as the Werner, isotropic and Bell diagonal states.
How the prepared states and Unruh effect affect Measurement-Induced-Nonlocality (MIN) is studied. We show that, as the Unruh temperature increases, the MIN between modes A and I decreases but the MIN between modes A and II increases. We prove that the parameters ci which decide initial prepared states affect not only the values of the MIN, but also the dynamical behavior of it. By comparing the MIN with the maximal expectation values of CHSH inequality and geometric discord between modes A and I, we also find that the MIN is more general than the quantum nonlocality related to violation of Bell's inequalities, and its values is always equal or bigger than that of the geometric discord.