Linear response theory of entanglement entropy

Wang，Yuan Sheng1,2; Ma，Teng3; Yung，Man Hong4

2022-08-01

10.1016/j.physa.2022.127437

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS   影响因子和分区

0378-4371

1873-2119

Linear response theory (LRT) is a powerful tool for investigating classical and quantum systems when perturbed by some external forces, connecting experimental observables with the correlation functions of the system in equilibrium states. On the other hand, the entanglement entropy (EE), or von Neumann entropy, is an important measure of non-classical correlations in quantum information science. As the EE is not a normal physical observable, developing a LRT for EE is valuable for understanding the changes of entanglement under an external perturbation. In this work, we present a framework of LRT of the von Neumann entropy. We found that for any composite quantum state the linear response of the von Neumann entanglement entropy can be quantified by a special correlation function. Consequently, we can derive the corresponding Kubo formula and the susceptibility of the EE, which have the same properties as its conventional counterpart. We further found that the linear response of the EE is zero for maximally entangled or separable states, a unique feature of entanglement dynamics. A numerical verification of our analytical results is also given based on the XX spin chain model. Overall, the LRT of EE provides a useful tool in investigating and understanding EE.

Entanglement entropy Linear response Non equilibrium Open quantum system Quantum information Quantum physics

EI ; SCI

英语

其他

National Natural Science Foundation of China[11875160];National Natural Science Foundation of China[11905100];Economy, Trade and Information Commission of Shenzhen Municipality[201901161512];National Natural Science Foundation of China[U1801661];

Physics

Physics, Multidisciplinary

WOS:000879481200011

ELSEVIER

20222012116010

Entropy ; Quantum entanglement

Thermodynamics:641.1 ; Light/Optics:741.1 ; Quantum Theory; Quantum Mechanics:931.4

PHYSICS

2-s2.0-85129941464

Scopus

1.School of Systems Science,Beijing Normal University,Beijing,100875,China
2.Department of Physics,Southern University of Science and Technology,Shenzhen,518055,China
3.Beijing Academy of Quantum Information Sciences,Beijing,100193,China
4.Institute for Quantum Science and Engineering,and Department of Physics,Southern University of Science and Technology,Shenzhen,518055,China

Wang，Yuan Sheng,Ma，Teng,Yung，Man Hong. Linear response theory of entanglement entropy[J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS,2022,599.

Wang，Yuan Sheng,Ma，Teng,&Yung，Man Hong.(2022).Linear response theory of entanglement entropy.PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS,599.

Wang，Yuan Sheng,et al."Linear response theory of entanglement entropy".PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 599(2022).