It was recently shown that black holes decohere any quantum superpositions in their vicinity. This decoherence is mediated by soft radiation through the horizon, and can be understood as the result of the fact that quantum states in the exterior source distinguishable states of long-range fields in the interior. To study this phenomenon and others, we extend Tomita-Takesaki theory to accommodate states of soft radiation such as arise in the electromagnetic and gravitational memory effects, and provide a general framework for computing the distinguishability of general coherent states. Applying these tools, we use the methods of unambiguous state discrimination and approximate quantum error correction to prove some new relations regarding the distinguishability of quantum states, and the quantum information content of soft radiation, and thereby show that a black hole (or any horizon) decoheres its environment as though its interior were full of optimal observers.
32 pages, 2 figures. v2: Strengthened the bound of Eq. (29), corrected an error in the proof of Eq. (A17), and fixed several typos. Version to appear in Phys. Rev. D
It was recently shown that black holes decohere any quantum superpositions in their vicinity. This decoherence is mediated by soft radiation through the horizon, and can be understood as the result of the fact that quantum states in the exterior source distinguishable states of long-range fields in the interior. To study this phenomenon and others, we extend Tomita-Takesaki theory to accommodate states of soft radiation such as arise in the electromagnetic and gravitational memory effects, and provide a general framework for computing the distinguishability of general coherent states. Applying these tools, we use the methods of unambiguous state discrimination and approximate quantum error correction to prove some new relations regarding the distinguishability of quantum states, and the quantum information content of soft radiation, and thereby show that a black hole (or any horizon) decoheres its environment as though its interior were full of optimal observers.
We consider an experimentalist, Alice, who creates a quantum superposition of a charged or massive body outside of a black hole (or, more generally, in the presence of a Killing horizon). It was previously shown that emission of soft photons/gravitons into the black hole will result in the decoherence of the components of the superposition if it is held open for a sufficiently long span of time. However, at any finite time, t c , during the process, it is not obvious how much decoherence has irrevocably occurred. Equivalently, it is not obvious how much information an observer inside the black hole can extract about Alice’s superposition prior to time t c . In this paper, we solve for the optimal experimental protocol to be followed by Alice for t > t c so as to minimize the decoherence of the components of her superposition. More precisely, given the entangling radiation that has passed through the horizon prior to the cross-section C corresponding to the time t = t c in Alice’s lab, we determine the “optimal purification” of this radiation beyond C such that the global quantum state of the radiation through the horizon has maximal overlap (quantum fidelity) with the Hartle-Hawking or Unruh vacuum. Due to the intricate low frequency entanglement structure of the quantum field theory vacuum state, we find this optimal purification to be nontrivial. In particular, even if Alice has already “closed” her superposition by bringing the components back together, we find that she can decrease the net decoherence of the components of her superposition somewhat by reopening it and performing further manipulations.
We recently showed that if a massive (or charged) body is put in a quantum spatial superposition, the mere presence of a black hole in its vicinity will eventually decohere the superposition. In this paper we show that, more generally, decoherence of stationary superpositions will occur in any spacetime with a Killing horizon. This occurs because, in effect, the long-range field of the body is registered on the Killing horizon which, we show, necessitates a flux of ``soft horizon gravitons/photons'' through the horizon. The Killing horizon thereby harvests ``which path'' information of quantum superpositions and will decohere any quantum superposition in a finite time. It is particularly instructive to analyze the case of a uniformly accelerating body in a quantum superposition in flat spacetime. As we show, from the Rindler perspective the superposition is decohered by ``soft gravitons/photons'' that propagate through the Rindler horizon with negligible (Rindler) energy. We show that this decoherence effect is distinct from---and larger than---the decoherence resulting from the presence of Unruh radiation. We further show that from the inertial perspective, the decoherence is due to the radiation of high frequency (inertial) gravitons/photons to null infinity. (The notion of gravitons/photons that propagate through the Rindler horizon is the same notion as that of gravitons/photons that propagate to null infinity.) We also analyze the decoherence of a spatial superposition due to the presence of a cosmological horizon in de Sitter spacetime. We provide estimates of the decoherence time for such quantum superpositions in both the Rindler and cosmological cases. Although we explicitly treat the case of spacetime dimension d=4, our analysis applies to any dimension $d\ensuremath{\ge}4$.
We show that if a massive body is put in a quantum superposition of spatially separated states, the mere presence of a black hole in the vicinity of the body will eventually destroy the coherence of the superposition. This occurs because, in effect, the gravitational field of the body radiates soft gravitons into the black hole, allowing the black hole to acquire “which path” information about the superposition. A similar effect occurs for quantum superpositions of electrically charged bodies. We provide estimates of the decoherence time for such quantum superpositions. We believe that the fact that a black hole will eventually decohere any quantum superposition may be of fundamental significance for our understanding of the nature of black holes in a quantum theory of gravity.
This paper proposes that black holes can be described as globally coherent quantum systems, despite the emission of Hawking radiation. While the Hawking process induces a weak coupling between the interior and exterior regions, this interaction is demonstrated to be too small to produce significant decoherence for macroscopic and supermassive black holes. By treating the event horizon as a quasi-isolated, semi-transparent quantum interface, this framework reconciles semiclassical gravity with quantum unitarity. The black hole and its emitted radiation are modeled as a single, entangled pure quantum state that evolves unitarily. Key contributions of this work include: Formalization of the black hole-radiation system as a coherent quantum cavity. Mathematical derivation showing that the decoherence rate scales as Γ_dec ∝ M⁻⁸. Demonstration that for astrophysical black holes, the decoherence time τ_D is astronomically larger than the evaporation time t_evap, implying that global quantum coherence is effectively preserved. A potential resolution to the black hole information paradox within a unitary evolution framework. This research contributes to the ongoing theoretical discussion on the nature of event horizons, quantum information, and the holographic principle. Acknowledgements: I would like to express my deepest gratitude to my beloved dog, Milo, and my father, for their constant support, encouragement, and companionship throughout the development of this research.
There is mounting theoretical evidence that black hole horizons induce decoherence on a quantum system, say a particle, put in a superposition of locations, with the decoherence functional, evaluated after closure of the superposition, increasing linearly with the time the superposition has been kept open. This phenomenon has been shown to owe its existence to soft modes, that is modes with very low frequencies, of the quantum fields---sourced by the particle---which pierce through the horizon, or also can be understood as coming from the interaction with the black hole described as a thermodynamic quantum system at Hawking's temperature. Here we investigate the effects of ensuing quantum aspects of the geometry itself of the horizon, in an effective perspective in which the quantum geometry of the horizon is captured by the existence of a limit length or by a horizon area quantization. We show that the discreteness of the energy levels associated to the different geometric configurations might have a strong impact on the results, in particular reducing the decoherence effects even to a negligible level in the case of quanta of area A0=O(1)lp2 or larger, with lp the Planck length.
Recent work by Danielson, Satishchandran, and Wald (DSW) has shown that black holes—and, in fact, Killing horizons more generally—impart a fundamental rate of decoherence on all nearby quantum superpositions. The effect can be understood from measurement and causality: An observer (Bob) in the black hole should be able to disturb outside quantum superpositions by measuring their superposed gravitational fields, but since his actions cannot (by causality) have this effect, the superpositions must automatically disturb themselves. DSW calculated the rate of decoherence up to an unknown numerical factor for distant observers in Schwarzschild spacetime, Rindler observers in flat spacetime, and static observers in de Sitter spacetime. Working in electromagnetic and Klein-Gordon analogs, we flesh out and generalize their calculation to derive a general formula for the precise decoherence rate for Killing observers near bifurcate Killing horizons. We evaluate the rate in closed form for an observer at an arbitrary location on the symmetry axis of a Kerr black hole. This fixes the numerical factor in the distant-observer Schwarzschild result, while allowing new exploration of near-horizon and/or near-extremal behavior. In the electromagnetic case we find that the decoherence vanishes entirely in the extremal limit, due to the “black hole Meissner effect” screening the Coulomb field from entering the black hole. This supports the causality picture: Since Bob is unable to measure the field of the outside superposition, no decoherence is necessary—and indeed none occurs. Published by the American Physical Society 2024