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International Journal of Theoretical Physics

Quantum Teleportation via Entangled State of Light in Schwarzschild Black Hole

Sevda Mirzaei, Amin Rezaei Akbarieh

Published Oct 23, 2020• 3 citations
Publisher

Abstract

Abstract In this paper, we describe the properties of quantum entanglement and teleportation between Alice and Bob who is freely falling toward the Schwarzschild black hole. To this aim, in the flat Minkowski spacetime before a black hole is formed, Alice and Bob share a two-mode entangled coherent state (ECS) generated by Kerr medium and the beam splitter. We will show that the degree of entanglement decreases with increasing the radius of black hole r. Moreover, the fidelity of quantum teleportation via ECS, as a quantum channel, is also reduced because of the Hawking-Unruh effect.

DOI
10.1007/s10773-020-04618-7

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Abstract In this paper, we describe the properties of quantum entanglement and teleportation between Alice and Bob who is freely falling toward the Schwarzschild black hole. To this aim, in the flat Minkowski spacetime before a black hole is formed, Alice and Bob share a two-mode entangled coherent state (ECS) generated by Kerr medium and the beam splitter. We will show that the degree of entanglement decreases with increasing the radius of black hole r. Moreover, the fidelity of quantum teleportation via ECS, as a quantum channel, is also reduced because of the Hawking-Unruh effect.
We study the properties of quantum entanglement and teleportation in the background of stationary and rotating curved spacetimes with extra dimensions. We show that a maximally entangled Bell state in an inertial frame becomes less entangled in curved space due to the well-known Hawking–Unruh effect. The degree of entanglement is found to be degraded with the increase in the extra dimensions. For a finite black hole surface gravity, the observer may choose a higher frequency mode to keep high level entanglement. The fidelity of quantum teleportation is also reduced because of the Hawking–Unruh effect. We discuss the fidelity as a function of extra dimensions, mode frequency, black hole mass and black hole angular momentum parameter for both bosonic and fermionic resources.
A bstract Previous studies have shown that the Hawking effect always destroys quantum correlations and the fidelity of quantum teleportation in the Schwarzschild black hole. Here, we investigate the fidelity of quantum teleportation of Dirac fields between users in Schwarzschild spacetime. We find that, with the increase of the Hawking temperature, the fidelity of quantum teleportation can monotonically increase, monotonically decrease, or non-monotonically increase, depending on the choice of the initial state, which means that the Hawking effect can create net fidelity of quantum teleportation. This striking result banishes the extended belief that the Hawking effect of the black hole can only destroy the fidelity of quantum teleportation. We also find that quantum steering cannot fully guarantee the fidelity of quantum teleportation in Schwarzschild spacetime. This new unexpected source may provide a new idea for the experimental evidence of the Hawking effect.
We analyze the entanglement degradation provoked by the Hawking effect in a bipartite system Alice-Rob when Rob is in the proximities of a Schwarzschild black hole while Alice is free falling into it. We will obtain the limit in which the tools imported from the Unruh entanglement degradation phenomenon can be used properly, keeping control on the approximation. As a result, we will be able to determine the degree of entanglement as a function of the distance of Rob to the event horizon, the mass of the black hole, and the frequency of Rob's entangled modes. By means of this analysis we will show that all the interesting phenomena occur in the vicinity of the event horizon and that the presence of event horizons do not effectively degrade the entanglement when Rob is far off the black hole. The universality of the phenomenon is presented: There are not fundamental differences for different masses when working in the natural unit system adapted to each black hole. We also discuss some aspects of the localization of Alice and Rob states. All this study is done without using the single mode approximation.
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.
Final state of a black hole is studied by taking into account a general unitary evolution of a black hole matter state. It is found that the mixedness decreases under general unitary transformation when the initial matter state was in mixed state and the mean fidelity at the evaporation is smaller than the fidelity of the quantum teleportation by the factor of inverse square of the number of states of a black hole. The change of entanglement Alice-Bob pair at evaporation is also studied by calculating the entanglement fidelity and eigenvalues of the partial transposed block density matrix. We assumed that Alice fell onto the black hole when the hole was formed while Bob is maintaining the safe distance from the black hole. It is found that the entanglement fidelity is inversely proportional to the square of the Hilbert space dimension N and the entanglement can survive the evaporation process.
Abstract The merging of quantum information science with the relativity theory presents novel opportunities for understanding the enigmas surrounding the transmission of information in relation to black holes. For this purpose, we study the quantumness near a Schwarzschild black hole in a practical model under decoherence. The scenario we consider in this paper is that a stationary particle in the flat region interacts with its surroundings while another particle experiences free fall in the vicinity of a Schwarzschild black hole’s event horizon. We explore the impacts of Hawking radiation and decoherence on the system under investigation and find that these effects can limit the survival of quantum characteristics, but cannot destroy them completely. Hence, the results of this study possess the potential to yield valuable insights into the comprehension of the quantum properties of a real system operating within a curved space-time framework.