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arXiv:2507.16911 · Physical review. D/Physical review. D.

Effects of quantum geometry on the decoherence induced by black holes

Max Joseph Fahn, A. Pesci

Published Oct 30, 2025• 2 citations
arXivHTMLPDF

Abstract

Recently, it has been shown that a quantum system held in spatial superposition and then eventually recombined does experience decoherence from black hole horizons, at a level increasing linearly with the time the superposition has been kept open. In this, the effects of the horizon have been derived using a classical spacetime picture for the latter. In the present paper we point out that quantum aspects of the geometry itself of the quantum black hole could significantly affect the results. In a specific effective implementation of the quantum geometry in terms of a minimal length and ensuing minimal area, it appears in particular that, for selected values of the quantum of area proposed on various grounds in the literature, the decoherence induced by the horizon turns out to be limited to negligibly small values.

DOI
10.1103/279x-zgl1

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Recently, it has been shown that a quantum system held in spatial superposition and then eventually recombined does experience decoherence from black hole horizons, at a level increasing linearly with the time the superposition has been kept open. In this, the effects of the horizon have been derived using a classical spacetime picture for the latter. In the present paper we point out that quantum aspects of the geometry itself of the quantum black hole could significantly affect the results. In a specific effective implementation of the quantum geometry in terms of a minimal length and ensuing minimal area, it appears in particular that, for selected values of the quantum of area proposed on various grounds in the literature, the decoherence induced by the horizon turns out to be limited to negligibly small values.
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{A}_{0}=\mathcal{O}(1){l}_{p}^{2}A0​=O(1)lp2​ or larger, with lp{l}_{p}lp​ the Planck length.
We study the decoherence induced by near-extremal charged black holes on quantum systems in their exterior. Specifically, we analyze a thought experiment recently discussed in the literature, where the quantum system is a charged particle prepared in a spatial superposition. Near-extremal black holes are known to exhibit large quantum metric fluctuations of the near-horizon geometry at low temperatures. We show that, at late times, if the black hole is sufficiently close to extremality, these quantum gravity effects make the decoherence rate vanish. This phenomenon is due to a spin-induced energy gap in the quantum black hole spectrum. For energies above the gap, the decoherence rate becomes nonzero, but is still suppressed relative to semiclassical expectations, so these quantum gravity effects always enhance the coherence of the superposition.
It was previously shown that if an experimenter, Alice, puts a massive or charged body in a quantum spatial superposition, then the presence of a black hole (or more generally any Killing horizon) will eventually decohere the superposition. This decoherence was identified as resulting from the radiation of soft photons/gravitons through the horizon, thus suggesting that the global structure of the spacetime is essential for describing the decoherence. In this paper, we show that the decoherence can alternatively be described in terms of the local two-point function of the quantum field within Alice’s lab, without any direct reference to the horizon. From this point of view, the decoherence of Alice’s superposition in the presence of a black hole arises from the extremely low frequency Hawking quanta present in Alice’s lab. We explicitly calculate the decoherence occurring in Schwarzschild spacetime in the Unruh vacuum from the local viewpoint. We then use this viewpoint to elucidate (i) the differences in decoherence effects that would occur in Schwarzschild spacetime in the Boulware and Hartle-Hawking vacua; (ii) the difference in decoherence effects that would occur in Minkowski spacetime filled with a thermal bath as compared with Schwarzschild spacetime; (iii) the lack of decoherence in the spacetime of a static star even though the vacuum state outside the star is similar in many respects to the Boulware vacuum around a black hole; and (iv) the requirements on the degrees of freedom of a material body needed to produce a decoherence effect that mimics that of a black hole.
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=4d=4d=4, our analysis applies to any dimension $d\ensuremath{\ge}4$.
Recently, it was discussed how the presence of a Killing horizon induces decoherence on a quantum system in a superposition of states. Focusing on the case of an electrically-charged system with superposed positions, this would happen due to ``entangling'' photons crossing the horizon while carrying information on the superposition. Purpose of this essay is to investigate this process in connection with black hole thermodynamics and the ensuing entropy bounds. We show that an apparent tension arising with the latter is resolved provided the entangling photons, expressing a modification of the field at, as well as inside the horizon, do not give rise to a flux across it. The storage of information in this field, not retrievable from an outside observer, causes the superposition to decohere.
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.