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arXiv:2304.07847 · Advanced Quantum Technologies

Tripartite Entanglement Extraction from the Black Hole Vacuum

Ireneo James Membrere, Kensuke Gallock‐Yoshimura, Laura J. Henderson, Robert B. Mann

Published Jul 24, 2023• 10 citations
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Abstract

Abstract The first investigation of tripartite entanglement harvesting in the vicinity of a black hole is carried out. Working in the context of a static Bañados–Teitelboim–Zanelli (BTZ) black hole spacetime the authors find that it is possible to harvest tripartite entanglement in regions where harvesting of bipartite entanglement is known to be impossible due to intense Hawking radiation. In these situations, it implies that the harvested entanglement is of the Greenberger–Horne–Zeilinger (GHZ) type.

DOI
10.1002/qute.202300125

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•Oct 4, 2018•0 citations
Abstract The first investigation of tripartite entanglement harvesting in the vicinity of a black hole is carried out. Working in the context of a static Bañados–Teitelboim–Zanelli (BTZ) black hole spacetime the authors find that it is possible to harvest tripartite entanglement in regions where harvesting of bipartite entanglement is known to be impossible due to intense Hawking radiation. In these situations, it implies that the harvested entanglement is of the Greenberger–Horne–Zeilinger (GHZ) type.
We investigate the correlation harvesting protocol for mutual information between two Unruh-DeWitt detectors in a static Ba\~nados-Teitelboim-Zanelli black hole spacetime. Here, the effects coming from communication and change in proper separation of the detectors are set to be negligible so that only a black hole affects the extracted mutual information. We find that, unlike the entanglement harvesting scenario, harvested mutual information is zero only when a detector reaches an event horizon, and that although the Hawking effect and gravitational redshift both affect the extraction of mutual information, it is extreme Hawking radiation that inhibits the detectors from harvesting.
A bstract The effect of black holes on entanglement harvesting has been of considerable interest over the past decade. Research involving stationary Unruh-DeWitt (UDW) detectors near a (2+1)-dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole has uncovered phenomena such as entanglement shadows, entanglement amplification through black hole rotation, and differences between bipartite and tripartite entanglement. For a (1+1)-dimensional Schwarzschild black hole, it has been shown that two infalling UDW detectors can harvest entanglement from the scalar quantum vacuum even when separated by an event horizon. In this paper, we calculate the mutual information between two UDW detectors coupled to a massless quantum scalar field, with the detectors starting at rest and falling radially into a non-rotating (2+1)-dimensional BTZ black hole. The trajectory of the detectors includes regions where both detectors are switched on outside of the horizon; where one detector is switched on inside of the horizon while the other switches on outside; and where both detectors switch on inside of the horizon. We investigate different black hole masses, detector energy gaps, widths and temporal separations of the detector switching functions, and field boundary conditions. We find that black holes — even the simplest kind having constant curvature — significantly affect the correlation properties of quantum fields in the vacuum state. These correlations, both outside and inside the horizon, can be mapped out by infalling detectors.
We carry out the first investigation of the entanglement and mutual information harvesting protocols for detectors freely falling into a black hole. Working in (1+11+11+1)-dimensional Schwarzschild black hole spacetime, we consider two pointlike Unruh-DeWitt detectors in different combinations of free-falling and static trajectories. Employing a generalization of relative velocity suitable for curved spacetimes, we find that the amount of correlations extracted from the black hole vacuum, at least outside the near-horizon regime, is largely kinematic in origin (i.e., it is mostly due to the relative velocities of the detectors). Second, correlations can be harvested purely from the black hole vacuum even when the detectors are causally disconnected by the event horizon. Finally, we show that the previously known `entanglement shadow' near the horizon is indeed absent for the case of two free-falling-detectors, since their relative gravitational redshift remains finite as the horizon is crossed, in accordance with the equivalence principle.
Abstract We implement the entanglement harvesting protocol, in which two Unruh–DeWitt detectors become entangled through local interactions with a quantum field, for the first time in the vicinity of a black hole. Our study, focusing on the BTZ black hole, reveals that black holes inhibit entanglement harvesting. For two detectors with fixed proper separation along the radial direction, we demonstrate that the entanglement harvested rapidly falls to zero as the detectors move closer to the horizon. This effect is a combination of black hole radiation and gravitational redshift, both generic properties of horizons, suggesting it is a general result for black holes.
Abstract The quantum vacuum has long been known to be characterized by field correlations between spacetime points. We show that such correlations—vacuum entanglement—in the environment of near-extremal black holes is significantly amplified (up to ten-fold) relative to their slowly rotating counterparts. We demonstrate this effect for rotating Banados–Teitelboim–Zanelli black holes by measuring the entanglement through the concurrence extracted from the vacuum via two-level quantum systems (Unruh–DeWitt detectors). The effect is manifest at intermediate distances from the horizon, and is most pronounced for near-extremal small mass black holes. The effect is also robust, holding for all boundary conditions of the field and at large spacelike detector separations. Smaller amplification occurs near the horizon, where we find that the entanglement shadow—a region near the black hole from which entanglement cannot be extracted—is diminished in size as the black hole’s angular momentum increases.
The aim of this work is present the phenomenon denoted entanglement harvesting.We begin by introducing entanglement historically.Following, we go beyond the one particle theory in flat spacetime and introduce Quantum Field Theory in Curved Spacetime, showing two famous consequences: the Unruh effect and the Hawking radiation.Finally, we analyze entanglement harvesting for two Unruh-deWitt detectors.In the fisrt example, we see that there is a "sudden death" point of entanglement harvesting when the detectors are near the BTZ black hole event horizon, due to redshift effect and Hawking radiation.Then, we compare the phenomenon for different scenarios, and find out that it is sensitive to the structure of spacetime.Finally, we see how detectors' parameters affect it and find out that the smoothness of the switching of the detectors' coupling to the field is extremely relevant.We also see how the parameters can be used to optimize entanglement harvested.