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Quantum Backflow Across A Black Hole Horizon

Dripto Biswas, Subir Ghosh

Published May 9, 2021• 0 citations
OpenAlex

Abstract

In this paper, we study quantum backflow across the event horizon of a Schwarzschild Black Hole. As a preliminary study, we superpose two radially ingoing solutions and observe the probability current. We explicitly demonstrate a non-vanishing quantum backflow in a small region around the event horizon. This is in contrast to the classical black hole picture that once an excitation crosses the horizon, it is lost forever from the outside world. Deeper implications of this phenomenon are speculated.

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In this paper, we study quantum backflow across the event horizon of a Schwarzschild Black Hole. As a preliminary study, we superpose two radially ingoing solutions and observe the probability current. We explicitly demonstrate a non-vanishing quantum backflow in a small region around the event horizon. This is in contrast to the classical black hole picture that once an excitation crosses the horizon, it is lost forever from the outside world. Deeper implications of this phenomenon are speculated.
Quantum backflow, discovered quite a few years back, is a generic purely quantum phenomenon, in which the probability of finding a particle in a direction is nonzero (and increasing for a certain period of time) even when the particle has with certainty a velocity in the opposite direction. In this paper, we study quantum backflow of a quantum particle across the event horizon of a Schwarzschild black hole. In a toy model approach, we consider a superposition of two ingoing solutions and observe the probability density and probability current. We explicitly demonstrate a nonvanishing quantum back flow in a small region around the event horizon. This is in contrast to the classical black hole picture, that once an excitation crosses the horizon, it is lost forever from the outside world. Deeper implications of this phenomenon are speculated. We also study quantum backflow for another spacetime with horizon, the Rindler spacetime, where the phenomenon can be studied only within the Rindler wedge.
We investigate the Hawking effect on entangled fields. By considering a scalar field which is in a two-mode squeezed state from the point of view of freely falling (Kruskal) observers crossing the horizon of a Schwarzschild black hole, we study the degradation of quantum and classical correlations in the state from the perspective of physical (Schwarzschild) observers confined outside the horizon. Due to monogamy constraints on the entanglement distribution, we show that the lost bipartite entanglement is recovered as multipartite entanglement among modes inside and outside the horizon. In the limit of a small-mass black hole, no bipartite entanglement is detected outside the horizon, while the genuine multipartite entanglement interlinking the inner and outer regions grows infinitely.
We investigate quantum characteristics around Schwarzschild black hole, exploring various quantum resources and their interplay in curved space-time. Our analysis reveals intriguing behaviors of quantum coherence, global and genuine multipartite entanglement, first-order coherence, and mutual information in different scenarios. Initially, we consider three particles shared among Alice, Bob, and Charlie in a Minkowski space far from the event horizon, where these particles are correlated via Greenberger-Horne-Zeilinger-type correlation. While Alice's particle remains in Minkowski space, Bob and Charlie accelerate towards the event horizon, experiencing black hole evaporation and generating antiparticles correlated via the Hawking effect. We employ the Kruskal basis formulation to derive a pentapartite pure state shared among particles inside and outside the event horizon. Investigating different scenarios among particles both inside and outside the event horizon, we observe how quantum resources evolve and distribute among consideration of different particles with Hawking temperature and mode frequency. The trade-off relationship between first-order coherence and concurrence fill persists, indicating the intricate interplay between coherence and entanglement. Notably, the mutual information between external observers and particles inside the black hole becomes nonzero, deepening our understanding of quantum effects in curved space-time and shedding light on the quantum nature of the black hole. We believe that these findings will pave the way for future investigations into the fundamental quantum mechanical aspects of gravity under extreme environments.
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.
It is shown that the internal stationary state of the Schwarzschild black hole can be represented by a maximally entangled two-mode squeezed state of collapsing matter and infalling Hawking radiation. The final boundary condition at the singularity is then described by the random unitary transformation acting on the collapsing matter field. The outgoing Hawking radiation is obtained by the final-state projection on the total wave function, which looks like a quantum teleportation process without the classical information transmitted. The black hole evaporation process as seen by the observer outside the black hole is now a unitary process but nonlocal physics is required to transmit the information outside the black hole. It is also shown that the final-state projection by the evaporation process is strongly affected by the quantum state outside the event horizon, which clearly violates the locality principle.