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arXiv:0907.0485 · Physical Review A

Sudden death of entanglement and teleportation fidelity loss via the Unruh effect

André G. S. Landulfo, George E. A. Matsas

Published Sep 15, 2009• 109 citations
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Abstract

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.

DOI
10.1103/physreva.80.032315

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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.
Quantum decoherence, which appears when a system interacts with its environment in an irreversible way, plays a fundamental role in the description of quantum-to-classical transitions and has been successfully applied in some important experiments. Here, we study the decoherence in noninertial frames. It is shown that the decoherence and loss of the entanglement generated by the Unruh effect will influence each other remarkably. It is interesting to note that, in the case of the total system under decoherence, the sudden death of entanglement may appear for any acceleration. However, in the case of only Rob's qubit undergoing decoherence, sudden death may only occur when the acceleration parameter is greater than a ``critical point.''
The interaction of an accelerated observer with a quantum field can modify the entanglement and quantum information shared between observers, thereby affecting quantum communication in non-inertial frames. We formulate the standard teleportation protocol in a relativistic setting where Alice remains inertial while Rob undergoes uniform acceleration and is modeled as an Unruh-DeWitt detector locally coupled to a massive scalar field. The detector-field interaction initially leads to a loss of entanglement and quantum information shared between Alice and Rob. Remarkably, under acceleration, the anti-Unruh regime can reverse this degradation, leading to an increase in both the shared entanglement and the accessible quantum information. We further find that, in the anti-Unruh regime, the teleportation fidelity is independent of the local free-evolution time of Alice's and Rob's states. At high accelerations, the recovered entanglement and quantum information enhance the teleportation fidelity, which approaches unity under appropriate conditions. These results demonstrate that the anti-Unruh effect can protect and recover quantum entanglement and information in a non-inertial frame by reducing the detector's effective temperature and the associated decoherence.
It is commonly believed that the fidelity of quantum teleportation using localized quantum objects with one party or both accelerated in vacuum would be degraded due to the heat up by the Unruh effect. In this paper, we point out that the Unruh effect is not the whole story in accounting for all the relativistic effects in quantum teleportation. First, there could be degradation of fidelity by a common field environment even when both quantum objects are in inertial motion. Second, relativistic effects entering the description of the dynamics, such as frame dependence, time dilation, and Doppler shift, already existent in inertial motion, can compete with or even overwhelm the effect due to uniform acceleration in a quantum field. We show it is not true that larger acceleration of an object would necessarily lead to a faster degradation of fidelity. These claims are based on four cases of quantum teleportation we studied using two Unruh--DeWitt detectors coupled via a common quantum field initially in the Minkowski vacuum. We find the quantum entanglement evaluated around the light cone, rather than the conventional ones evaluated on the Minkowski time slices, is the necessary condition for the averaged fidelity of quantum teleportation beating the classical one. These results are useful as a guide to making judicious choices of states and parameter ranges and estimation of the efficiency of quantum teleportation in relativistic quantum systems under environmental influences.
It is well known that the quantum fluctuation of entanglement (QFE) between Unruh–De Witt detector (modeled by a two-level atom) is always investigated in a relativistic setting. However, both of the Unruh radiation and quantum fluctuation effects play an important role in precise measurements of quantum entanglement. In this paper, we have quantitatively analyzed how the relativistic motion affects the QFE for two entangled Unruh–De Witt detectors, one of which is accelerated and interacting with the neighbor external scalar field. Our results show that the QFE, which initially increases by the Unruh thermal noise, will suddenly decay when the acceleration reaches to a considerably large value. Therefore, the relativistic effect will lead to non-negligible QFE effect. We also find that the initial QFE (without acceleration effect) reaches its minimum value at the maximally entangled state and the separable state. More importantly, our analysis demonstrates that although the QFE has a huge decay when the acceleration is greater than ∼0.96, the ratio of ΔE/C is still very large, due to the simultaneous decay of concurrence to a very low value. Finally, enlightened by the well-known equivalence principle, we discuss the possibility of applying the above findings to the dynamics of QFE under the influence of gravitation field.
We study the effects of decoherence on the entanglement generated by Unruh effect in accelerated frames by using various combinations of an amplitude damping channel, a phase damping channel and a depolarizing channel in the form of multilocal and collective environments. Using concurrence as entanglement quantifier, we show that the occurrence of entanglement sudden death (ESD) depends on different combinations of the channels. The ESD can be avoided under a particular configuration of the channels. We show that the channels can be used to distinguish between a moving and a stationary frame.