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Journal of Physics A Mathematical and Theoretical

Mixed-state entanglement in noninertial frames

Xing Mao Xiao, Mao-Fa Fang

Published Mar 11, 2011• 16 citations
Publisher

Abstract

The entanglement between two modes of a free scalar field (or a free Dirac field) is investigated in noninertial frames under the condition that they are initially prepared in a Werner state. It is found that the entanglement degradation induced by the Unruh effect highly depends on the initial purity f and the type of fields. For a fixed acceleration r , the critical values of f for the states entangled or separable are obtained in both scalar and Dirac fields. Finally, we make a comparison between the entanglement and the quantum discord and show that quantum discord is more robust than entanglement in our models.

DOI
10.1088/1751-8113/44/14/145306

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The entanglement between two modes of a free scalar field (or a free Dirac field) is investigated in noninertial frames under the condition that they are initially prepared in a Werner state. It is found that the entanglement degradation induced by the Unruh effect highly depends on the initial purity f and the type of fields. For a fixed acceleration r , the critical values of f for the states entangled or separable are obtained in both scalar and Dirac fields. Finally, we make a comparison between the entanglement and the quantum discord and show that quantum discord is more robust than entanglement in our models.
The entanglement between two modes of free scalar and Dirac fields as seen by two relatively accelerated observers has been investigated. It is found that the same initial entanglement for an initial state parameter $\ensuremath{\alpha}$ and its ``normalized partner'' $\sqrt{1\ensuremath{-}{\ensuremath{\alpha}}^{2}}$ will be degraded by the Unruh effect along two different trajectories except for the maximally entangled state, which just shows the inequivalence of the quantization for a free field in Minkowski and Rindler coordinates. In the infinite-acceleration limit, the state does not have distillable entanglement for any $\ensuremath{\alpha}$ for the scalar field, but always remains entangled to a degree that is dependent on $\ensuremath{\alpha}$ for the Dirac field. It is also interesting to note that in this limit the mutual information equals just half of the initial mutual information; this result is independent of $\ensuremath{\alpha}$ and the type of field.
Abstract Using the single-mode approximation we study the quantum correlations of a free Dirac field on the Werner state in the noninertial frame. We present analytical quantum discord D and its geometric measurement D G . We notice that the quantum discord still exists for the system ρ ARI even in the acceleration limit. We also calculate the entanglement of formation (EOF) and the geometric measure of entanglement ( E G ) to compare the behaviors of the entanglement with the quantum discord. The entanglement is nonzero for the fidelity of the Werner state with a Bell state F > 0.5, while the quantum discord is equal to zero only for F = 0.25. We also observe that the quantum discord is more robust to the change of acceleration than the entanglement, which is more sensitive to the acceleration.
We analyze the entanglement between two modes of a free Dirac field as seen by two relatively accelerated parties. The entanglement is degraded by the Unruh effect and asymptotically reaches a nonvanishing minimum value in the infinite acceleration limit. This means that the state always remains entangled to a degree and can be used in quantum information tasks, such as teleportation, between parties in relative uniform acceleration. We analyze our results from the point of view afforded by the phenomenon of entanglement sharing and in terms of recent results in the area of multiqubit complementarity.
In this paper, some concepts of quantum correlations, such as one-way quantum deficit, purity, and entanglement of formation are investigated between the modes of Dirac fields in noninertial frames. We consider two bipartite divisions of a tripartite system constructed by initial Werner states, which is shared between two relatively accelerated observers. The degradation of these quantum correlations is shown when the acceleration parameter increases. However, a nonzero amount of correlations survives even at infinite acceleration limit. Furthermore, we study the inevitable influence of mixedness factor of initial state on the quantum correlations behaviour. Finally, we review our calculation beyond single-mode approximation and point out some differences and similarities between the two regimes.
We calculate the quantum discord between two free modes of a scalar field, which start in a maximally entangled state and then undergo a relative constant acceleration. In a regime where there is no distillable entanglement due to the Unruh effect, we show that there is a finite amount of quantum discord, which is a measure of purely quantum correlations in a state over and above quantum entanglement. Even in the limit of infinite acceleration of the observer detecting one of the modes, we provide evidence for a nonzero amount of purely quantum correlations. We discuss our result in the context of secure quantum communications involving eavesdroppers in noninertial frames.
The classical and quantum correlation sharing between modes of Dirac fields in the noninertial frame are investigated. It is shown that (i) the classical correlation for the Dirac fields decreases as the acceleration increases, which is different from the result in a scalar field, where the classical correlation is independent of the acceleration; (ii) there is no simple dominating relation between the quantum correlation and entanglement for the Dirac fields, which is unlike the scalar case, where the quantum correlation is always over and above the entanglement; (iii) as the acceleration increases, the correlations between modes I and II and between modes AAA and II increase, but the correlations between modes AAA and I decrease.