Monogamy of Measurement Induced Non-Locality

TL;DR

This paper investigates the monogamy properties of measurement-induced nonlocality in multi-qubit states, revealing that monogamy can be violated or satisfied depending on the state class, with extensions to larger systems.

Contribution

It provides the first detailed analysis of monogamy relations for measurement-induced nonlocality across various multi-qubit states, including counterexamples and extensions to n-qubits.

Findings

GHZ and W states satisfy monogamy in three-qubit systems

Violations of monogamy occur in certain GHZ-class and W-class states

Most four-qubit states in the generic class satisfy monogamy, with exceptions like GHZ

Abstract

Measurement-Induced NonLocality was introduced by Luo and Fu (Phys. Rev. Lett. \textbf{106}, 120401,(2011)) as a measure of nonlocality in a bipartite state. In this paper we will discuss monogamy property of measurement-induced nonlocality for some three- and four-qubit classes of states. Unlike discord, we find quite surprising results in this situation. Both the GHZ and W states satisfy monogamy relations in the three-qubit case, however, in general there are violations of monogamy relations in both the GHZ-class and W-class states. In case of four-qubit system, monogamy holds for most of the states in the generic class. Four qubit GHZ does not satisfy monogamy relation, but W-state does. We provide several numerical results including counterexamples regarding monogamy nature of measurement induced nonlocality. We will also extend our results of generalized W-class to n-qubit.