Abstract
We study the dynamics of Gaussian quantum steering in the background of a Garfinkle–Horowitz–Strominger dilaton black hole. It is found that the gravity induced by dilaton field will destroy the quantum steerability between the inertial observer Alice and the observer Bob who hovers outside the event horizon, while it generates steering-type quantum correlations between the causally disconnected regions. Therefore, the observers can steer each other’s state by local measurements even though they are separated by the event horizon. Unlike quantum entanglement in the dilaton spacetime, the quantum steering experiences catastrophic behaviors such as “sudden death” and “sudden birth” with increasing dilaton charge. In addition, the dilaton gravity destroys the symmetry of Gaussian steering and the latter is always asymmetric in the dilation spacetime. Interestingly, the attainment of maximal steering asymmetry indicates the critical point between one-way and two-way steering for the two-mode Gaussian state in the dilaton spacetime.
Highlights
String theory is a promising candidate for a consistent theory of quantum mechanics and theory of gravitation
We study the distribution and asymmetry of Gaussian quantum steering in the background of a GHS
The steering between Alice and Bob suffers from a “sudden death” before the dilaton charge approaches the mass of the black hole
Summary
String theory is a promising candidate for a consistent theory of quantum mechanics and theory of gravitation. We investigate the Gaussian quantum steering and its symmetrical property under the influence of a GHS dilaton black hole. 2 we discuss the scalar field dynamics and second quantization near the GHS dilaton black hole. 4 we study the distribution and asymmetry of Gaussian quantum steerability in GHS dilaton black holes. Solving the Klein-Gordon near the event horizon r = r+ of the GHS black hole, one obtains the outgoing modes inside and outside the event horizon φout,ωlm (r < r+) = eiωu Ylm (θ, φ),. Where bin,ωlm and bi†n,ωlm are the annihilation and creation operators acting on the states of the interior region of the dilaton black hole. By second-quantizing the scalar field in terms of φI,ωlm and φI I,ωlm in the GHS spacetime, one can define the Kruskal vacuum |0 K aK,ωlm |0 K = 0,.
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