Nonlocality is one unique property of quantum mechanics that differs from the classical world. One of its quantifications can be properly described as the maximum global effect caused by locally invariant measurements, known as measurement-induced nonlocality (MIN) (2011 Phys. Rev. Lett. 106 120401). Here, we propose quantifying the MIN by the trace norm. We show explicitly that this measure is monotonically decreasing under the action of a completely positive trace-preserving map, which is the general local quantum operation, on the unmeasured party for the bipartite state. This property avoids the undesirable characteristic appearing in the known measure of MIN defined by the Hilbert–Schmidt norm which may be increased or decreased by trivial local reversible operations on the unmeasured party. We obtain analytical formulas of the trace-norm MIN for any -dimensional pure state, two-qubit state, and certain high-dimensional states. As with other quantum correlation measures, the newly defined MIN can be directly applied to various models for physical interpretations.
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.
We investigate quantum correlations in a hybrid qubit-qutrit system subject to both axial and planar single-ion anisotropies, dipolar spin-spin interactions, and Dzyaloshinskii-Moriya (DM) coupling. Using Negativity, Measurement-Induced Non-locality (MIN), Uncertainty-Induced Nonlocality (UIN), and Bell nonlocality (as quantified by the CHSH inequality) as measures, we analyze the interplay between anisotropy parameters, magnetic fields, and temperature on the survival of quantum correlations. Our results demonstrate that Bell nonlocality and entanglement (Negativity) are highly sensitive to temperature and anisotropy, exhibiting sudden death under thermal noise, whereas MIN and UIN are significantly more robust. In particular, these discord-like and information-theoretic measures provide the largest baseline and persist even in parameter regions where entanglement vanishes, highlighting their suitability as a quantumness witness in realistic conditions. Notably, our Bell nonlocality study is tailored to the asymmetric qubit-qutrit setting by exploiting a recently developed qubit-qudit CHSH maximization framework. However, Bell nonlocality is confirmed to be the most fragile, surviving only in narrow parameter windows at low temperature. A key finding of this work is that we observe the fragility hierarchy: Bell nonlocality
⊆ Negativity
⊆ UIN(MIN) in the qubit-qutrit setting. These results provide deeper insight into the relative robustness of distinct quantum resources in anisotropic qubit-qutrit models, suggesting that quantum discord-like measures, such as MIN and UIN, may serve as more practical resources than entanglement for quantum information tasks in thermally active spin systems.
We introduce a quantum Fisher information based measurement-induced nonlocality (QFI-MIN), which quantifies the maximal statistical distinguishability induced by locally invariant unitary dynamics. The proposed measure inherits desirable properties including positivity, local unitary invariance, monotonicity under local operations, and immunity to the local ancilla problem. Analytical expressions are obtained for pure states, arbitrary two-qubit states, and two-qubit X states, revealing a direct connection with entanglement for pure systems. We further establish clear operational interpretations of QFI-MIN in quantum parameter estimation, local channel discrimination, and correlation-assisted communication. Its behavior under amplitude damping, depolarizing, and generalized amplitude damping channels demonstrates robustness against environmental noise. The proposed framework provides a physically consistent and operationally meaningful quantifier of quantum correlations, linking nonlocality, quantum metrology, and quantum information processing