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arXiv:0910.1715

Quantum Teleportation with an Accelerated Observer and Black Hole Information

K. Shiokawa

Published Oct 9, 2009• 3 citations
arXivHTMLPDF

Abstract

Nonperturbative analysis of quantum entanglement and quantum teleportation protocol using oscillator variables carried by observers in relativistic motion under the continuous influence of the environment is given. The full time evolution of quantum entanglement among static and accelerated observers is studied. The environment plays a dual role. While it creates bipartite and tripartite entanglement among observers even when the initial state is separable, it suppresses the entanglement via decoherence. Motivated by the black hole information problem, we consider quantum teleportation between static and accelerated observers. Acceleration of the observer suppresses fidelity of teleportation. Some of the quantum information escapes outside of the horizon in the form of bipartite and tripartite entanglement during the teleportation process. Explicit calculation of information loss is provided. In addition to the loss due to the interaction with the environment, there is an intrinsic loss originated in a measurement process. We discuss the implications of our results on the black hole case.

DOI
10.48550/arxiv.0910.1715

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Nonperturbative analysis of quantum entanglement and quantum teleportation protocol using oscillator variables carried by observers in relativistic motion under the continuous influence of the environment is given. The full time evolution of quantum entanglement among static and accelerated observers is studied. The environment plays a dual role. While it creates bipartite and tripartite entanglement among observers even when the initial state is separable, it suppresses the entanglement via decoherence. Motivated by the black hole information problem, we consider quantum teleportation between static and accelerated observers. Acceleration of the observer suppresses fidelity of teleportation. Some of the quantum information escapes outside of the horizon in the form of bipartite and tripartite entanglement during the teleportation process. Explicit calculation of information loss is provided. In addition to the loss due to the interaction with the environment, there is an intrinsic loss originated in a measurement process. We discuss the implications of our results on the black hole case.
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.
Efficiencies of quantum information protocols can be affected by the noninertial motion of involved parties, e.g., in a gravitational field. Most of the previous studies focused on the effects of such a motion on a bipartite entanglement as a resource. We show how a tripartite Gaussian resource state of continuous variables is affected by the acceleration of the observers. Specifically, we analyze how genuine tripartite entanglement degrades due to the motion for various initial states and trajectories of the involved parties.
Abstract We investigate the robustness of quantum teleportation in the presence of strong gravitational fields by analyzing bipartite mixed states derived from tripartite GHZ and W -class states near black hole event horizons. Considering a scenario where two observers approach the horizon of either a Schwarzschild or a Garfinkle–Horowitz–Strominger Dilaton black hole while a third remains in flat space, we quantify the teleportation fidelity of the resulting bipartite channels after tracing out one party. Through the quantization of Dirac fields and Bogoliubov transformations, we compute the teleportation fidelity under the influence of Hawking radiation and spacetime curvature. Our results show that while entanglement degrades, teleportation fidelity remains above the classical threshold of f > 2 3 for channels derived from W -class states, but not for GHZ -derived states. This indicates that quantum teleportation can remain feasible near black holes provided the initial entangled state retains useful bipartite entanglement.
Abstract In this paper quantum teleportation of an unknown quantum state via noisy maximally bipartite (Bell) and maximally tripartite (Greenberger–Horne–Zeilinger (GHZ)) entangled states are investigated. We suppose that one of the observers who would receive the sent state accelerates uniformly with respect to the sender. The interactions of the quantum system with its environment during the teleportation process impose noises. These (unital and nonunital) noises are: phase damping, phase flip, amplitude damping and bit flip. In expressing the modes of the Dirac field used as qubits, in the accelerating frame, the so-called single mode approximation is not imposed. We calculate the fidelities of teleportation, and discuss their behaviors using suitable plots. The effects of noise, acceleration and going beyond the single mode approximation are discussed. Although the Bell states bring higher fidelities than GHZ states, the global behaviors of the two quantum systems with respect to some noise types, and therefore their fidelities, are different.
The effect of the Hawking temperature on the entanglement and teleportation for the scalar field in a most general, static, and asymptotically flat black hole with spherical symmetry has been investigated. It has been shown that the same ``initial entanglement'' for the state parameter $\ensuremath{\alpha}$ and its ``normalized partners'' $\sqrt{1\ensuremath{-}{\ensuremath{\alpha}}^{2}}$ will be degraded by the Hawking effect with increasing Hawking temperature along two different trajectories except for the maximally entangled state. In the infinite Hawking temperature limit, corresponding to the case of the black hole evaporating completely, the state no longer has distillable entanglement for any $\ensuremath{\alpha}$. It is interesting to note that the mutual information in this limit is equal to just half of the ``initially mutual information.'' It has also been demonstrated that the fidelity of teleportation decreases as the Hawking temperature increases, which indicates the degradation of entanglement.
We study an exactly solvable model where a uniformly accelerated detector is linearly coupled to a massless scalar field initially in the Minkowski vacuum. Using the exact correlation functions obtained in Lin and Hu (2006 Phys. Rev. D 73 124018, 2007 Phys. Rev. D 76 064008) we show that as soon as the coupling is switched on one can see information flowing from the detector to the field and propagating with the radiation into null infinity. By expressing the reduced density matrix of the detector in terms of the two-point functions, we calculate the purity function in the detector and study the evolution of quantum entanglement between the detector and the field. Only in the ultraweak coupling regime could some degree of recoherence in the detector appear at late times, but never in full restoration. We explicitly show that under the most general conditions the detector never recovers its quantum coherence and the entanglement between the detector and the field remains large at late times. To the extent that this model can be used as an analog to the system of a black hole interacting with a quantum field, our result seems to suggest in the prevalent non-Markovian regime, assuming unitarity for the combined system, that black hole information is not lost but transferred to the quantum field degrees of freedom. Our combined system will evolve into a highly entangled state between a remnant of large area (in Bekenstein's black hole atom analog) without any information of its initial state, and the quantum field, now imbued with complex information content not-so-easily retrievable by a local observer.