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arXiv:1512.04886 · Physical review. D/Physical review. D.

Quantum entanglement in three accelerating qubits coupled to scalar fields

Yue Dai, Zhejun Shen, Yu Shi

Published Jul 7, 2016• 34 citations
arXivHTMLPDF

Abstract

We consider quantum entanglement of three accelerating qubits, each of which is locally coupled with a real scalar field, without causal influence among the qubits or among the fields. The initial states are assumed to be the GHZ and W states, which are the two representative three-partite entangled states. For each initial state, we study how various kinds of entanglement depend on the accelerations of the three qubits. All kinds of entanglement eventually suddenly die if at least two of three qubits have large enough accelerations. This result implies the eventual sudden death of all kinds of entanglement among three particles coupled with scalar fields when they are sufficiently close to the horizon of a black hole.

DOI
10.1103/physrevd.94.025012

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We consider quantum entanglement of three accelerating qubits, each of which is locally coupled with a real scalar field, without causal influence among the qubits or among the fields. The initial states are assumed to be the GHZ and W states, which are the two representative three-partite entangled states. For each initial state, we study how various kinds of entanglement depend on the accelerations of the three qubits. All kinds of entanglement eventually suddenly die if at least two of three qubits have large enough accelerations. This result implies the eventual sudden death of all kinds of entanglement among three particles coupled with scalar fields when they are sufficiently close to the horizon of a black hole.
We consider two entangled accelerating qubits coupled with real scalar fields, each described by the Unruh-Wald model. It is demonstrated that because of the Unruh effect of the fields, the bipartite entanglement between the two qubits suddenly dies when the acceleration of one or more qubits are large enough. We also consider three entangled accelerating qubits in GHZ state and in W state, with equal acceleration-frequency ratio, and found that in either state, the tripartite entanglement suddenly dies at a certain value of acceleration-frequency ratio. The equivalence between the Rindler metric and the Schwarzschild metric in the vicinity of the horizon of a black hole implies that for two entangled qubits outside a black hole, the entanglement suddenly dies when one or both of the qubits are close enough to the horizon, while the three entangled qubits in GHZ or W state, the tripartite entanglement suddenly dies when these qubits are close enough to the horizon.
We study entanglement dynamics for a six-qubit model in cavity QED, where three two-level atoms A , B and C are initially prepared in a Greenberger–Horne–Zeilinger (GHZ)-like state and locally coupled with the independent cavities a , b and c , respectively. We consider entanglement evolution via negativity for the tripartite subsystems of atoms and the corresponding cavities. By choosing two types of GHZ-like states as atomic initial states, we shall show that the entanglement of atoms may or may not exhibit entanglement sudden death (ESD) depending on the type of atomic initial state.
In this article, we consider the entanglement between three identical qubits resonantly interacting with a thermal field of an Q-infinite resonator. We derived the exact solution of the evolution equation for density matrix of the considered system. On it basis we calculate the negativity as a criteria of entanglement between pairs of qubits for biseparable and entangled W-type states of qubits. The results showed that for considered initial qubits states the effect of the entanglement sudden death occurs for all values of the average number of thermal photons.
We investigated the entanglement dynamics in a quantum system consisting of three two-level atoms resonantly coupled to a single mode electromagnetic field. We considered the dynamics of the system under consideration for Fock and thermal initial cavity states. An explicit analytical solution of the system has been obtained and the entanglement has been studied with the help of the two-qubit negativity. It was also shown that for both initial cavity states the sudden death of two-qubit entanglement takes place.
We use the Unruh effect to investigate how the teleportation of quantum states is affected when one of the entangled qubits used in the process is under the influence of some external force. In order to reach a comprehensive understanding, a detailed analysis of the acceleration effect on such entangled qubit system is performed. In particular, we calculate the mutual information and concurrence between the two qubits and show that the latter has a ``sudden death'' at a finite acceleration, whose value will depend on the time interval along which the detector is accelerated.
We review the results obtained by investigating, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups, the time evolution of quantum entanglement of two different bimodal systems, each one interacting with a thermal environment. The first system is formed of the free massless bosonic mode of a stationary observer in a region that is asymptotically flat (Kruskal observer) or freely falling in Schwarzschild black hole, and the mode of a uniformly accelerated observer hovering outside the event horizon of black hole. For initial bimodal Gaussian squeezed thermal states of the system, we show that under the influence of Hawking radiation the quantum entanglement of the two modes is destroyed in a finite time, for non-zero values of the temperature of the thermal environment, i.e. the phenomenon of entanglement sudden death takes place. The second system consists of two bosonic modes associated with a scalar quantum field in de Sitter space, characterized by two regions that are causally disconnected and described using open universe coordinates on two open charts. The survival time of the entanglement of this bimodal system strongly depends on the competition between the contrary effects provided by the squeezing of the initial bimodal state, the curvature of de Sitter space, the mass parameter and the thermal environment. It is shown that the entanglement is minimized for values 1/2 and 3/2 of the mass parameter, corresponding to the conformally coupled scalar field and, respectively, minimally coupled massless field.