Understanding quantum entanglement by thermo field dynamics

TL;DR

This paper introduces a novel approach using thermo field dynamics to better understand quantum entanglement, allowing distinction between intrinsic entanglement and thermal effects in both equilibrium and non-equilibrium states.

Contribution

It develops a new method with an extended density matrix in double Hilbert space to analyze quantum entanglement more clearly than traditional approaches.

Findings

Can distinguish intrinsic quantum entanglement from thermal fluctuations.

Applicable to both equilibrium and non-equilibrium states.

Provides a general formulation for the extended density matrix.

Abstract

We propose a new method to understand quantum entanglement using the thermo field dynamics (TFD) described by a double Hilbert space. The entanglement states show a quantum-mechanically complicated behavior. Our new method using TFD makes it easy to understand the entanglement states, because the states in the tilde space in TFD play a role of tracer of the initial states. For our new treatment, we define an extended density matrix on the double Hilbert space. From this study, we make a general formulation of this extended density matrix and examine some simple cases using this formulation. Consequently, we have found that we can distinguish intrinsic quantum entanglement from the thermal fluctuations included in the definition of the ordinary quantum entanglement at finite temperatures. Through the above examination, our method using TFD can be applied not only to equilibrium states but also to non-equilibrium states. This is shown using some simple finite systems in the present paper.