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Communications in Theoretical Physics

Fluctuations of Entanglement Entropy in Noninertial Frames

Cuihong Wen, Jieci Wang

Published Sep 1, 2014• 2 citations
Publisher

Abstract

The fluctuation and relative fluctuation of entanglement entropy of a bipartite system for Dirac fields in noninertial frames are investigated. It is shown that the fluctuation and relative fluctuation of entanglement entropy are observer-dependent, which depend on their observed frames. It is found that both the fluctuation and relative fluctuation of entanglement entropy become more noticeable with the increasing of the subsystem's acceleration. We also find that the entanglement entropy always has fluctuation regardless of the initial state parameter and for any magnitude of the acceleration. We argue that the statistical mean for the measurement of entanglement entropy relates to the accelerated motion of the observer.

DOI
10.1088/0253-6102/62/3/06

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The fluctuation and relative fluctuation of entanglement entropy of a bipartite system for Dirac fields in noninertial frames are investigated. It is shown that the fluctuation and relative fluctuation of entanglement entropy are observer-dependent, which depend on their observed frames. It is found that both the fluctuation and relative fluctuation of entanglement entropy become more noticeable with the increasing of the subsystem's acceleration. We also find that the entanglement entropy always has fluctuation regardless of the initial state parameter and for any magnitude of the acceleration. We argue that the statistical mean for the measurement of entanglement entropy relates to the accelerated motion of the observer.
Quantum coherence as the fundamental characteristic of quantum physics, provides the valuable resource for quantum computation in exceeding the power of classical algorithms. The exploration of quantum coherence in relativistic systems is of significance from both the fundamental points of view and practical applications. We investigate the quantum coherence of two free modes of scalar and Dirac fields as detected by two relatively accelerated observers by resorting to the relative entropy of coherence. We show that the relative entropy of coherence monotonically decreases when acceleration goes up, as a consequence of the Unruh effect. Specifically, the initial states with parameters α=bα=bα=b and α=1−b2α=\sqrt{1-b^2}α=1−b2​ have the same initial relative entropy coherence at a=0a=0a=0 (with aaa the acceleration), but degrade along two different trajectories. The relative entropy of coherence reaches vanishing value in the scalar field in the infinite acceleration limit, but non-vanishing value in the Dirac field. This suggests that in the Dirac field, the bipartite state possesses quantum coherence to some extent with the variation of the relative acceleration, and may lead to potential applications in quantum computation performed by observers in motion relatively.
Abstract Via using l 1-norm of quantum coherence and π–tangle, we investigate influences of amplitude-damping and depolarizing channels on quantum coherence and entanglement for W state of Dirac fields when two observers are in accelerating motion. We find that quantum entanglement vanishes for all values of acceleration if at least one qubit is under noisy channels. But quantum coherence does not vanish even at infinite acceleration if only one subsystem is under noisy channels. We also find that, unlike the depolarizing environment, the amplitude-damping environment can destroy symmetric properties of quantum entanglement with respect to two accelerated observers. These results will further enrich our understanding on the relation between quantum coherence and entanglement.
We present the entanglement measures of a tetrapartite W-class entangled system in a noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied. Two cases are considered. First, when one qubit has uniform acceleration whilst the other three remain stationary. Second, when two qubits have nonuniform accelerations and the others stay inertial. The 1–1 tangle, 1–3 tangle, and whole entanglement measurements π 4 and Π 4 , are studied and illustrated with graphics through their dependence on the acceleration parameter r d for the first case and r c and r d for the second case. It is found that the negativities (1–1 tangle and 1–3 tangle) and π-tangle decrease when the acceleration parameter r d or in the second case r c and r d increase, remaining a nonzero entanglement in the majority of the results. This means that the system will be always entangled except for special cases. It is shown that only the 1–1 tangle for the first case vanishes at infinite accelerations, but for the second case the 1–1 tangle disappears completely when r > 0.472473 . An analytical expression for the von Neumann information entropy of the system is found and we note that it increases with the acceleration parameter.
Using the single-mode approximation, we first calculate entanglement measures such as negativity (1–3 and 1–1 tangles) and von Neumann entropy for a tetrapartite W-Class system in noninertial frame and then analyze the whole entanglement measures, the residual π 4 and geometric Π 4 average of tangles. Notice that the difference between π 4 and Π 4 is very small or disappears with the increasing accelerated observers. The entanglement properties are compared among the different cases from one accelerated observer to four accelerated observers. The results show that there still exists entanglement for the complete system even when acceleration r tends to infinity. The degree of entanglement is disappeared for the 1–1 tangle case when the acceleration r > 0.472473. We reexamine the Unruh effect in noninertial frames. It is shown that the entanglement system in which only one qubit is accelerated is more robust than those entangled systems in which two or three or four qubits are accelerated. It is also found that the von Neumann entropy S of the total system always increases with the increasing accelerated observers, but the S κξ and S κζδ with two and three involved noninertial qubits first increases and then decreases with the acceleration parameter r , but they are equal to constants 1 and 0.811278 respectively for zero involved noninertial qubit.
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.