Tridiagonal Toeplitz Matrices and Bipartite Quantum Correlations

TL;DR

This paper studies how specific tridiagonal Toeplitz Hermitian matrices influence quantum correlations like entanglement and discord in bipartite states, revealing the roles of matrix off-diagonal elements and differences in state sensitivities.

Contribution

It demonstrates that off-diagonal terms in Toeplitz matrices significantly affect quantum correlation dynamics, and compares sensitivities of Werner states and MEMS to these effects.

Findings

Diagonal terms do not affect quantum correlations.

Super- and sub-diagonal terms influence correlation dynamics.

MEMS are more sensitive than Werner states.

Abstract

In this article, we focus on tridiagonal Toeplitz Hermitian matrices, which fulfill the requirement of a valid Hamiltonian often used in Quantum Information. We investigate the behavior of such matrices to pursue the dynamics of quantum correlations (entanglement and quantum discord) for bipartite Werner state and maximally entangled mixed states. We have found interesting results that the main diagonal terms in the Toeplitz matrices never affect the quantum correlations in both quantum states. However, super-diagonal and sub-diagonal terms play the important role in the dynamics. We investigate the phenomenon of entanglement sudden death and also observe the presence of quantum discord in the absence of entanglement. Most importantly it is found that MEMS is more sensitive in comparison to the Werner state.