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arXiv:2105.13520

Is quantum teleportation beyond horizon possible?

Jun-ichirou Koga, Kengo Maeda

Published May 28, 2021• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2105.13520

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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.
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.
An intriguing property of the massless quantum vacuum state is that it contains entanglement between both spacelike and timelike separated regions of space-time. The implications of timelike entanglement and its connection to standard entanglement, however, are unexplored. Here we show that timelike entanglement can be extracted from the massless Minkowski vacuum and converted into standard entanglement ``at a given time'' between two inertial, two-state detectors at the same spatial location: one coupled to the field in the past and the other coupled to the field in the future. The procedure used here demonstrates a time correlation as a requirement for extraction; e.g., if the past detector was active at a quarter to 12:00, then the future detector must wait to become active at precisely a quarter past 12:00 in order to achieve entanglement.
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.
We demonstrate that the future and left Rindler wedges of Minkowski spacetime are entangled, leading to the Unruh effect. Similarly, the past and right Rindler wedges are also entangled. We propose a protocol to extract this entanglement using two two-state detectors located in the past and right Rindler wedges. By scaling the detector transition frequencies inversely with Minkowski time, entanglement from the quantum field is transferred to the detectors, suggesting they may support quantum teleportation via the vacuum. Our protocol can be implemented with current quantum systems, such as flux-tunable transmon qubits. This research provides new insights into the entanglement properties of spacetime and hints at practical applications for secure quantum information transfer using the vacuum state of a quantum field.
We investigate the quantum teleportation between a conformal detector Alice and an inertial detector Bob in de Sitter space in two schemes, (i) one uses free scalar modes and (ii) one utilizes cavity to store qubit. We show that the fidelity of the teleportation is degraded for Bob in both cases. While the fidelity-loss is due to the Gibbons–Hawking effect associated with his cosmological horizon in the scheme (i), the entanglement decreases in the scheme (ii) because the ability to entangle the cavities is reduced by the spacetime curvature. With a cutoff at Planck-scale, comparing with the standard Bunch–Davies choice, we also show that the possible Planckian physics cause extra modifications to the fidelity of the teleportation protocol in both schemes.
We consider a pair of two-level Unruh-DeWitt detectors accelerated uniformly in the Minkowski vacuum of a massless neutral scalar field and analyze, within the perturbation theory, the entanglement extracted from the vacuum into the Unruh-DeWitt detectors when the switching of the detectors is performed adiabatically enough at the asymptotic past and future. We consider the cases where the detectors are accelerated parallelly, antiparallelly, and in differently orientated directions. We show that entanglement is extracted if they are accelerated antiparallelly and the ratios of the excitation energy to the magnitude of the acceleration coincide between the two detectors. On the other hand, we find that the detectors are not entangled when the detectors are accelerated parallelly or in orientated directions. We discuss these results from the viewpoint of the energy conservation associated with the timelike boost Killing vector fields tangent to the worldlines of the detectors.