Decoherence Effect of Qubits in 1D Transverse Ising Model

TL;DR

This paper analyzes how decoherence affects correlation functions in a 1D transverse Ising model, highlighting when higher-order correlations are necessary for accurate descriptions.

Contribution

It provides an analytical study of the role of higher-order correlation functions in qubit decoherence within the 1D transverse Ising model, identifying regimes where they are essential.

Findings

High-order correlations matter under strong coupling and long coherence times.

Low-order correlations suffice under weak coupling and short coherence times.

Classical Markov process approximation has limitations in certain regimes.

Abstract

With the development of lab technology, the low-order correlation function can no longer describe the main effect of decoherence in quantum many-body system, so it is imperative to study the higher-order correlation function of the system. In this paper, we study the changes of the correlation functions in the decoherence effect, analytically. And explore when it is possible to approach the qubit decoherence process only by low-order correlation function, and when third-order or higher correlation functions are needed in 1D transverse Ising model. It indicates that, under strong coupling and long coherence time, the effect of high-order correlation functions can not be ignored, and the approximation of classical Markov process is limited. But, in the case of weak coupling and short coherence time, low-order correlation function can describe well.