Investigation entanglement entropy in the coupled quantum harmonic oscillator model

Abstract

The definite and important role of entanglement in the study of quantum many-body systems has made it a special topic for numerous recent research. Various entanglement measures have been introduced and used by researchers to calculate the amount of entanglement between parts of a system. Some of these entanglement measures identify the amount of entanglement between two parts of the system, and the entanglement entropy is one of them. Entanglement entropy is the von Neumann entropy of the reduced density matrix of the system that has been studied in various bosonic and fermionic systems. One of the models for which entanglement entropy has been studied is the coupled quantum harmonic oscillator model. The importance of this model is because of the ground state of its Hamiltonian. The ground state of the coupled quantum harmonic oscillator Hamiltonian is a Gaussian state, and it is possible to implement quantum information processes such as quantum teleportation, quantum cryptography and quantum computing with great experimental success using Gaussian states.

In this thesis, the method of calculating the entanglement entropy for the ground state of the Hamiltonian of the coupled quantum harmonic oscillator is described. Then, the properties of the entanglement entropy are studied according to the increase in the number of oscillators in some kinds of partitions for some famous graphs, including the Complete graph, the Star graph, the Path graph, and the Cycle graph. Afterward, the entanglement entropy is investigated according to all possible kinds of partitions in the mentioned graphs.

Ms.C thesis, advisor: Dr. F. Eghbalifam