Distinguishing quantum dynamics via Markovianity and Non-Markovianity

TL;DR

This paper develops analytical methods to distinguish different quantum dynamics in XX spin chains by coupling an auxiliary qubit and measuring its properties, linking Markovianity and non-Markovianity.

Contribution

It introduces an analytical approach to connect quantum dynamics types with environment properties using a coupled qubit and extends the projection method with an open-system interaction picture.

Findings

Delocalized chains are Markovian, localized chains are non-Markovian.

Dephasing noise affects the chain's bath properties depending on dephasing strength.

Quantum dynamics can be distinguished by measuring a single qubit.

Abstract

To study various quantum dynamics, it is important to develop effective methods to detect and distinguish different quantum dynamics. A common non-demolition approach is to couple an auxiliary system (ancilla) to the target system, and to measure the ancilla only. By doing so, the target system becomes an environment for the ancilla. Thus, different quantum dynamics of target systems will correspond to different environment properties. Here, we analytically study XX spin chains presenting different kinds of quantum dynamics, namely localized, delocalized, and dephasing dynamics, and build connections between Markovianity and non-Markovianity-the two most common properties of an environment. For a qubit coupled to the XX chain, we derived the reduced density matrix of the qubit through the projection method. Furthermore, when dephasing noise was introduced to the XX chain, we generalized the projection method by introducing an open-system interaction picture - a modification of the Dirac interaction picture. By calculating the reduced density matrix for the qubit analytically and numerically, we found that the delocalized (localized) chain corresponds to the Markovian (non-Markovian) bath when boundary effects are not considered, and the feature of the chain with dephasing noise as a bath is dependent on the dephasing strength. The three kinds of quantum dynamics can be distinguished by measuring the qubit only.