Effect of Weak Measurement Reversal on Quantum Correlations in a Correlated Amplitude Damping Channel, with a Neural Network Perspective

TL;DR

This paper investigates how weak measurement reversal can preserve quantum correlations in noisy channels, compares single- and two-qubit protocols, and employs neural networks to predict quantum discord from other correlations.

Contribution

It introduces a two-qubit WMR protocol for better preservation of quantum correlations and applies neural networks to analyze and predict quantum discord from other measures.

Findings

Two-qubit WMR outperforms single-qubit in preserving correlations.

Neural network accurately predicts quantum discord from other correlations.

Concurrence and EPR steering significantly influence discord prediction.

Abstract

We study the evolution of quantum correlations in Bell, Werner, and maximally entangled mixed states of two qubits subjected to correlated amplitude-damping channels. Our primary focus is to evaluate the robustness of entanglement as a resource for quantum information protocols such as dense coding, teleportation, and Einstein-Podolsky-Rosen (EPR) steering under the influence of noise. In addition, we investigate the behaviour of other quantum correlations, including quantum discord and coherence, and analyze their hierarchy under decoherence. To counteract the detrimental effects of the channels, we apply the weak measurement and quantum measurement reversal (WMR) protocol, comparing the effectiveness of single-qubit and two-qubit WMR techniques. Our results show that the two-qubit WMR protocol significantly outperforms the single-qubit approach in preserving quantum correlations. Furthermore, we employ a neural network model to enhance our analysis of the relationship between different quantum correlation measures during the evolution. Using a MATLAB-based artificial neural network with 80 neurons across three hidden layers and trained with the Levenberg-Marquardt algorithm, we successfully predict trace distance discord from other correlations, achieving low prediction errors. Besides, our analysis of the neural network weights suggests that concurrence and EPR steering have the most positive influence on the accurate discord predictions.