Understanding quantum entanglement by thermo field dynamics

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.

24 pages, 6 figures accepted by Physica A (in press)

References in corpus (5)

• Entanglement versus Correlations in Spin Systems
• Valence Bond Entanglement Entropy
• Correlation amplitude and entanglement entropy in random spin chains
• Irreversibility and Entropy Production in Transport Phenomena I
• Entanglement Entropy in an Antiferromagnetic Heisenberg Spin Chain with Boundary Impurities

Cited by in corpus (5)

• Entanglement entropy and Fisher information metric for closed bosonic strings in homogeneous plane wave background
• Flavor vacuum entanglement in boson mixing
• Entanglement of higher-derivative oscillators in holographic systems
• A new perspective to formulate a dissipative thermo field dynamics
• Entanglement Entropies of Non-Equilibrium Finite-Spin Systems