# The dynamic behaviors of local quantum uncertainty for three-qubit X states under decoherence channels

## TL;DR

This paper analytically examines the behavior of local quantum uncertainty in three-qubit X-states, comparing it with other quantum correlations and analyzing its robustness and dynamics under various decoherence channels.

## Contribution

It provides the first analytical expressions for local quantum uncertainty in three-qubit X-states and explores its dynamics and monogamy properties under decoherence.

## Key findings

- LQU matches quantum discord in non-classical correlations.
- LQU is more robust than negativity under decoherence.
- LQU exhibits revival and frozen phenomena under phase reversal channels.

## Abstract

We derive the analytical expression of local quantum uncertainty for three-qubit X-states. We give also the expressions of quantum discord and the negativity. A comparison of these three quantum correlations quantifiers is discussed in the special cases of mixed GHZ states and Bell-type states. We find that local quantum uncertainty gives the same amount of non-classical correlations as are measured by entropic quantum discord and goes beyond negativity. We also discuss the dynamics of non-classical correlations under the effect of phase damping, depolarizing and phase reversal channels. We find the local quantum uncertainty shows more robustness and exhibits, under phase reversal effect, revival and frozen phenomena. The monogamy property of local quantum uncertainty is also discussed. It is shown that it is monogamous for three-qubit states.