Abstract
The projective measurements on a vacuum performed by Rob, who hovers near the event horizon of the Einstein–Gauss–Bonnet black hole, will result in an entangled state for Alice moving along a geodesic. We show that the entanglement of the produced state is greatly dependent on Rob’s projective measurements and the parameters of the black hole, such as the horizon radius \(r_H\), Gauss–Bonnet coefficient \(\alpha \) and dimension d of the spacetime. We also present the conditions for Alice to get the maximal entangled state in this process.
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References
Unruh, W.G.: Notes on black-hole evaporation. Phys. Rev. D 14, 870 (1976)
Unruh, W.G., Wald, R.M.: What happens when an accelerating observer detects a Rindler particle. Phys. Rev. D 29, 1047 (1984)
Wald, R.M.: Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamic. The University of Chicago Press (1994)
Soffel, M., Müller, B., Greiner, W.: Dirac particles in Rindler space. Phys. Rev. D 22, 1935 (1980)
Longhi, P., Soldati, R.: Unruh effect revisited. Phys. Rev. D 83, 107701 (2011)
Martín-Martínez, E., Fuentes, I., Man, R.B.: Using Berry’s phase to detect the Unruh effect at lower accelerations. Phys. Rev. Lett. 107, 131301 (2011)
Olson, S.J., Ralph, T.C.: Entanglement between the future and the past in the quantum vacuum. Phys. Rev. Lett. 106, 110404 (2011)
Peres, A., Terno, D.R.: Quantum information and relativity theory. Rev. Mod. Phys. 76, 93 (2004)
Alsing, P.M., Milburn, G.J.: Teleportation with a uniformly accelerated partner. Phys. Rev. Lett. 91, 180404 (2003)
Fuentes-Schuller, I., Mann, R.B.: Alice falls into a black hole: entanglement in noninertial frames. Phys. Rev. Lett. 95, 120404 (2005)
Martín-Martínez, E., León, J.: Quantum correlations through event horizons: fermionic versus bosonic entanglement. Phys. Rev. A 81, 032320 (2010)
Alsing, P.M., Fuentes-Schuller, I., Mann, R.B., Tessier, T.E.: Entanglement of Dirac fields in noninertia frames. Phys. Rev. A 74, 032326 (2006)
Wang, J., Jing, J.: Multipartite entanglement of fermionic systems in noninertial frames. Phys. Rev. A 83, 022314 (2011)
Tian, Z., Jing, J.: How the Unruh effect affects transition between classical and quantum decoherences. Phys. Lett. B 707, 264–271 (2012)
Tian, Z., Jing, J.: Geometric phase of two-level atoms and thermal nature of de Sitter spacetime. J. High Energy Phys. 04, 109 (2013)
Tian, Z., Wang, J., Fan, H., Jing, J.: Relativistic quantum metrology in open system dynamics. Sci. Rep. 5, 7946 (2015)
Liu, X., Tian, Z., Wang, J., Jing, J.: Inhibiting decoherence of two-level atom in thermal bath by presence of boundaries. Quantum Inf. Process. 15, 3677–3694 (2016)
Liu, X., Tian, Z., Wang, J., Jing, J.: Protecting quantum coherence of two-level atoms from vacuum fluctuations of electromagnetic field. Ann. Phys. 366, 102–112 (2015)
Yang, Y., Jing, J., Zhao, Z.: Enhancing estimation precision of parameter for a two-level atom with circular motion. Quantum Inf. Process. 18, 120 (2019)
Ge, X.-H., Kim, S.P.: Quantum entanglement and teleportation in higher dimensional black hole spacetimes. Class. Quantum Grav. 25, 075011 (2008)
Jing, L., Jing, J.: Generating entangled fermions by projective measurements in Gauss–Bonnet spacetime. Quantum Inf. Process. 20, 61 (2021)
Pan, Q., Jing, J.: Hawking radiation, enatanglement and teleportation in background of an asymptotically flat static black hole. Phys. Rev. D 78, 065015 (2008)
Pan, Q., Jing, J.: Degradation of nonmaximal entanglement of scalar and Dirac fields in noninertial frames. Phys. Rev. A 77, 024302 (2008)
Martín-Martínez, E., Garay, L.J., León, J.: Unveiling quantum entanglement degradation near a Schwarzschild black hole. Phys. Rev. D 82, 064006 (2010)
Wang, J., Pan, Q., Chen, S., Jing, J.: Entanglement of coupled massive scalar field in background of Dilaton black hole. Phys. Lett. B 677, 186–189 (2009)
Wang, J., Pan, Q., Jing, J.: Entanglement redistribution in the Schwarzschild spacetime. Phys. Lett. B 692, 202–205 (2010)
Esfahani, B.N., Shamirzaie, M., Soltani, M.: Reduction of entanglement degradation and teleportation improvement in Einstein–Gauss–Bonnet gravity. Phys. Rev. D 84, 025024 (2011)
Han, M., Olson, J.S., Dowling, J.P.: Generating entangled photons from the vacuum by accelerated measurements: quantum information theory meets the Unruh–Davies effect. Phys. Rev. A 78, 022302 (2008)
Ostapchuk, C.M., Mann, R.B.: Generating entangled fermions by accelerated measurements on the vacuum. Phys. Rev. A 79, 042333 (2009)
Wang, J., Pan, Q., Jing, J.: Projective measurements and generation of entangled Dirac particles in Schwarzschild Spacetime. Annals Phys 325, 1190–1197 (2010)
Dehghani, M.H.: Accelerated expansion of the universe in Gauss–Bonnet gravity. Phys. Rev. D 70, 064019 (2004)
Damour, T., Ruffini, R.: Black-hole evaporation in the Klein–Sauter–Heisenberg–Euler formalism. Phys. Rev. D 14, 332 (1976)
Sannan, S.: Heuristic derivation of the probability distributions of particles emitted by a black hole. Gen. Relat. Grav. 20, 239–246 (1988)
Zhao, Z., Gui, Y.X.: The connection between Unruh scheme and Damour–Ruffini scheme in Rindler space-time and \(\eta -\varepsilon \) space-time. Nuov. Cim. B 109, 355–361 (1994)
Birrell, N.D., Davies, P.C.W.: Quantum Field in Curved Space. Cambridge University Press, Cambridge (1982)
Barnett, S.M., Radmore, P.M.: Method in Theoretical Quantum Optics. Oxford University Press, New York (1997)
Ahn, D.: Final state boundary condition of the Schwarzschild black hole. Phys. Rev. D 74, 084010 (2006)
Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1–8 (1996)
Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Acknowledgements
This work was by the Grant of NSFC No. 12035005, and National Key Research and Development Program of China No. 2020YFC2201400.
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Jing, L., Jing, J. Bosonic entanglement generated by projective measurements in Einstein–Gauss–Bonnet black hole. Quantum Inf Process 22, 371 (2023). https://doi.org/10.1007/s11128-023-04121-y
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DOI: https://doi.org/10.1007/s11128-023-04121-y