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.Comment: 24 pages, 6 figures accepted by Physica A (in press

Quantum Entanglement in Coupled Lossy Waveguides Using SU(2) and SU(1, 1) Thermo-Algebras

“…Our method shows the usefulness of thermofield dynamics in quantum entanglement problems, quite orthogonal to the approach given in Ref. [25], and allows us to handle damping in entanglement generation properties. We propose to apply this formalism to coupled light-atom systems, to shed further light on the effect of damping on the generation of entanglement.…”

Quantum analysis applied to thermo field dynamics on dissipative systems

“…and M.S.) investigated quantum entanglements at finite temperatures [6]. As shown in these previous studies, the TFD formulations are very useful to study thermal effects.…”

“…Using the TFD formulations, some interesting aspects of physical states in condensed matter were proposed in the previous studies [6][7][8][9]. For example, one of the authors (M.S.)…”

A new perspective to formulate a dissipative thermo field dynamics

“…Recently, thermo field dynamics (TFD) [1][2][3][4] played a very useful and important role to study entanglements [5][6][7][8][9][10][11], Kondo effects [12], the entropy effect of a black hole [13,14] and non-equilibrium phenomena [5,6,[15][16][17]. We have to introduce a tilde space in order to study statistical properties using TFD.…”