Transverse Ising Model: Markovian evolution of classical and quantum correlations under decoherence

TL;DR

This paper investigates how quantum and classical correlations evolve under decoherence in the transverse Ising model, revealing signatures of quantum phase transitions through correlation dynamics in Markovian environments.

Contribution

It analyzes the dynamics of quantum and classical correlations under various decoherence channels in the TIM, identifying correlation behaviors that signal quantum phase transitions.

Findings

Quantum correlations can surpass classical correlations during phase-flip decoherence.

Certain correlation dynamics signal the occurrence of quantum phase transitions.

Different decoherence channels exhibit distinct correlation evolution patterns.

Abstract

The transverse Ising Model (TIM) in one dimension is the simplest model which exhibits a quantum phase transition (QPT). Quantities related to quantum information theoretic measures like entanglement, quantum discord (QD) and fidelity are known to provide signatures of QPTs. The issue is less well explored when the quantum system is subjected to decoherence due to its interaction, represented by a quantum channel, with an environment. In this paper we study the dynamics of the mutual information $I(\rho_{AB})$, the classical correlations $C(\rho_{AB})$ and the quantum correlations $Q(\rho_{AB})$, as measured by the QD, in a two-qubit state the density matrix of which is the reduced density matrix obtained from the ground state of the TIM in 1d. The time evolution brought about by system-environment interactions is assumed to be Markovian in nature and the quantum channels considered are amplitude damping, bit-flip, phase-flip and bit-phase-flip. Each quantum channel is shown to be distinguished by a specific type of dynamics. In the case of the phase-flip channel, there is a finite time interval in which the quantum correlations are larger in magnitude than the classical correlations. For this channel as well as the bit-phase-flip channel, appropriate quantities associated with the dynamics of the correlations can be derived which signal the occurrence of a QPT.