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International Journal of Quantum Information

QUANTUM DISCORD AND QUANTUM ENTANGLEMENT IN THE PRESENCE OF AN ASYMPTOTICALLY FLAT STATIC BLACK HOLE

Eylee Jung, Mi-Ra Hwang, DaeKil Park

Published Sep 1, 2013• 3 citations
Publisher

Abstract

In this work, the quantum discord and tripartite entanglement in the presence of an asymptotically flat static black hole are discussed. The total correlation, quantum discord, and classical correlation are found to exhibit decreasing behavior with increasing Hawking temperature. It is shown that the classical correlation is less than the quantum discord in the full range of Hawking temperature. The tripartite entanglements for Greenberger–Horne–Zeilinger (GHZ) and W-states also exhibit decreasing behavior with increasing Hawking temperature. When the Hawking temperature approaches the infinite limit, the tripartite entanglements of the GHZ and W-states reduce, in terms of the π-tangle, to 52% and 33% of the corresponding values in the flat space limit, respectively.

DOI
10.1142/s0219749913500615

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Quantum Discord and Quantum Entanglement in the Background of an Asymptotically Flat Static Black Holes

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The quantum discord and tripartite entanglement are discussed in the presence of an asymptotically flat static black holes. The total correlation, quantum discord and classical correlation exhibit decreasing behavior with increasing Hawking temperature. It is shown that the classical correlation is less than the quantum discord in the full range of Hawking temperature. The tripartite entanglements for Greenberger-Horne-Zeilinger and W-states also exhibit decreasing behavior with increasing Hawking temperature. At the infinite limit of Hawking temperature the tripartite entanglements for Greenberger-Horne-Zeilinger and W-states reduce to 52% and 33% of the corresponding values in the flat space limit, respectively.

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In this work, the quantum discord and tripartite entanglement in the presence of an asymptotically flat static black hole are discussed. The total correlation, quantum discord, and classical correlation are found to exhibit decreasing behavior with increasing Hawking temperature. It is shown that the classical correlation is less than the quantum discord in the full range of Hawking temperature. The tripartite entanglements for Greenberger–Horne–Zeilinger (GHZ) and W-states also exhibit decreasing behavior with increasing Hawking temperature. When the Hawking temperature approaches the infinite limit, the tripartite entanglements of the GHZ and W-states reduce, in terms of the π-tangle, to 52% and 33% of the corresponding values in the flat space limit, respectively.
The quantum discord and tripartite entanglement are discussed in the presence of an asymptotically flat static black holes. The total correlation, quantum discord and classical correlation exhibit decreasing behavior with increasing Hawking temperature. It is shown that the classical correlation is less than the quantum discord in the full range of Hawking temperature. The tripartite entanglements for Greenberger-Horne-Zeilinger and W-states also exhibit decreasing behavior with increasing Hawking temperature. At the infinite limit of Hawking temperature the tripartite entanglements for Greenberger-Horne-Zeilinger and W-states reduce to 52% and 33% of the corresponding values in the flat space limit, respectively.
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 investigate the geometric quantum discord of bipartite Werner states influenced by Hawking radiation in the quantum atmosphere of a Schwarzschild black hole. We find that the geometric quantum discord in the physically accessible region exhibits a nonmonotonic behavior: it first decreases and then increases as the normalized radial distance increases, while the discord in the physically inaccessible region shows the exact opposite trend. A pronounced extremum of geometric quantum discord occurs precisely at the position corresponding to the peak intensity of Hawking radiation. Furthermore, we find that the Hartle Hawking constant and the event horizon radius exert opposite effects on the strength of quantum correlation redistribution: a larger Hartle Hawking constant enhances the redistribution effect, whereas a larger event horizon radius suppresses it.
A comparison is made between normal discord, super quantum discord, and entanglement for the tripartite Greenberger-Horne-Zeilinger (GHZ)-type squeezed states. For this aim, we start by studying the behavior of quantum discord for tripartite GHZ-type squeezed states. Also, we verify the monotonicity of the super quantum discord according to weaker quantum measurements. This was done by manipulating the amount of quantum information lost during the disruption of our quantum system and by controlling the measurement strength. Furthermore, we calculate the entanglement for our system.
Abstract We study the genuine tripartite entanglement (GTE), one-tangle and two-tangle of W state of fermionic fields in the background of a Schwarzschild black hole. We find that, with the increase of the Hawking temperature, the GTE of W state first decreases and then tends to zero, while the GTE of GHZ state first decreases and then freezes. We also find that the Hawking effect can completely destroy the two-tangle of W state, while one-tangle first decreases and then the freezing phenomenon appears with the growth of the Hawking temperature. These results are helpful to guide us to select appropriate quantum states and quantum resources to deal with relativistic quantum information tasks.
We calculate the analytic expression for geometric measure of entanglement for arbitrary superposition of two NNN-qubit canonical orthonormal Greenberger-Horne-Zeilinger (GHZ) states and the same for two WWW states. In the course of characterizing all kinds of nonclassical correlations, an explicit formula for quantum discord (via relative entropy) for the former class of states has been presented. Contrary to the GHZ state, the closest separable state to the WWW state is not classical. Therefore, in this case, the discord is different from the relative entropy of entanglement. We conjecture that the discord for the NNN-qubit WWW state is log2N\mathrm{log}{}_{2}Nlog2​N.