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A New Approach to Quantum Entanglement by Thermofield Dynamics

Koichi Nakagawa

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

For the purpose of clarifying a new approach to understanding quantum entanglement using the thermofield dynamics, entanglement entropies of non-equilibrium finite-spin systems are examined for both traditional and extended cases.

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Study on the Entanglement of Non-Equilibrium Finite-Spin Systems Based on Thermo-Field Dynamics

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We study the Zeeman effect on entanglement of non-equilibrium finite-spin systems with external fields using a method based on thermofield dynamics (TFD).For this purpose, the extended density matrices and extended entanglement entropies of two systems with either noncompeting or competing external fields are calculated according to the dissipative von Neumann equation, and the numerical results are compared.Consequently, through the "twin-peaks" oscillations of the quantum entanglement, we have illustrated the Zeeman effect on the entanglement of non-equilibrium finite-spin systems with competing external fields in the TFD algorithm.

•Dec 10, 2018•0 citations
For the purpose of clarifying a new approach to understanding quantum entanglement using thermofield dynamics (TFD), entanglement entropies of non-equilibrium finite-spin systems are examined for both traditional and extended cases. The extended entanglement entropy, |S^\hat {S}S^|⁠, is derived, and it is found that the conditions for the maximum entangled state can be obtained through this approach. The capacity of the TFD-based method to distinguish between states in quantum systems is confirmed.
We apply a new method based upon thermofield dynamics (TFD) to study entanglement of finite-spin systems with non-competitive external fields for both equilibrium and non-equilibrium cases. For the equilibrium finite-spin systems, the temperature dependence of the extended density matrices is derived using this method, and the effect of non-competitive external field is demonstrated. For the non-equilibrium finite-spin systems, the time dependence of the extended density matrices and the extended entanglement entropies is derived in accordance with von Noumann equation, and the dissipative dynamics of the finite-spin systems is argued. Consequently, the applicability of the TFD-based method to describe entanglement is confirmed in both equilibrium and non-equilibrium cases with the external fieds.
We study the Zeeman effect on entanglement of non-equilibrium finite-spin systems with external fields using a method based on thermofield dynamics (TFD).For this purpose, the extended density matrices and extended entanglement entropies of two systems with either noncompeting or competing external fields are calculated according to the dissipative von Neumann equation, and the numerical results are compared.Consequently, through the "twin-peaks" oscillations of the quantum entanglement, we have illustrated the Zeeman effect on the entanglement of non-equilibrium finite-spin systems with competing external fields in the TFD algorithm.