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arXiv:1204.1525 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quantum teleportation between moving detectors

Shih-Yuin Lin, Chung-Hsien Chou, B. L. Hu

Published Apr 30, 2015• 32 citations

Abstract

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.

DOI: 10.1103/physrevd.91.084063

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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.

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.

We consider entanglement extraction into two two-level Unruh-DeWitt detectors from a vacuum of a neutral massless quantum scalar field in a four-dimensional space-time, where the general monopole coupling to the scalar field is assumed. Based on the reduced density matrix of the two detectors derived within the perturbation theory, we show that the single copy of the entangled pair of the detectors can be utilized in quantum teleportation, even when the detectors are separated acausally, while we observe no violation of the Bell--CHSH inequality. In the case of the Minkowski vacuum, in particular, we find that entanglement usable in quantum teleportation is extracted due to the special relativistic effect when the detectors are in a relative inertial motion, while it is not when they are comoving inertially and the switching of the detectors is executed adiabatically at infinite past and future.

While the Unruh effect has traditionally been studied under the assumption of uniform acceleration, a simplification motivated by experimental considerations, it is not necessarily true for all non-inertial motions. We propose a novel approach for the indirect detection of the Unruh effect without relying on the former restriction. Previous studies have shown that probing the decoherence of an Unruh-DeWitt detector can significantly reduce the acceleration required for observing the effect by several orders of magnitude compared to earlier proposals. Building on this idea, we develop a theoretical framework describing a non-inertial observer equipped with a detector undergoing non-uniform, time-dependent acceleration. We show that, in a non-uniformly accelerated Rindler spacetime, the particle distribution perceived in the Minkowski vacuum acquires a time-dependent modification of the standard Unruh spectrum. Furthermore, we demonstrate that the inclusion of quantum entanglement leads to a deformation of the Minkowski vacuum into squeezed states.

We investigate the interaction between a moving detector and a quantum field, especially about how the trajectory of the detector would affect the vacuum fluctuations when the detector moves in a quantum field (the Unruh effect). We focus on two moving detectors system for future application in quantum teleportation. We find that the trajectory of a uniformly accelerated detector in Rindler space cannot be extended to a trajectory in which a detector moves at constant velocity. Based on our previous work, we redo the calculations and find that a term is missing from past calculations, and we also find that there are some restrictions on the values for the parameters in the solutions. In addition, without inclusion of the missing term, the variance from the quantum field for the inertial detector will be zero and is unlikely in such a system. When all these points are combined, there is a difference in the two-point correlation function between the inertial detector and the accelerated detector in the early-time region. The influence of proper acceleration can be seen in the two-point correlation functions. This might play a role in the quantum teleportation process and be worth studying thoroughly.

We ask whether quantum teleportation from the outside to the inside of a horizon is possible, using entanglement extracted from a vacuum. We first calculate analytically, within the perturbation theory, entanglement extracted from the Minkowski vacuum into a pair of an inertial and an accelerated Unruh-DeWitt detectors, which are initially in the ground states and interact with a neutral massless scalar field for an infinitely long time. We find that entanglement can be extracted, but is "fragile", depending on adiabaticity of switching of the detectors at the infinite past and future. We then consider the standard scheme of quantum teleportation utilizing the extracted entanglement, and find that the standard teleportation is not superior to channels without entanglement.

Abstract We study, in the framework of open quantum systems, the entanglement dynamics for a quantum system composed of two uniformly accelerated Unruh-Dewitt detectors interacting with a bath of massive scalar fields in the Minkowski vacuum. We find that the entanglement evolution for the quantum system coupled with massive fields is always slower compared with that of the one coupled with massless fields, and this time-delay effect brought about by the field being massive can however be counteracted by a large enough acceleration, in contrast to the case of a static quantum system in a thermal bath, where this time delay is not affected by the temperature. Remarkably, the maximal concurrence of the quantum system generated during evolution may increase with acceleration for any inter-detector separation while that for static ones in a thermal bath decreases monotonically with temperature, and this can be considered as an anti-Unruh effect in terms of the entanglement generated.