How to Minimize the Decoherence Caused by Black Holes (2501.04773v1)

Abstract: 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 $\mathcal C$ corresponding to the time $t = t_c$ in Alice's lab, we determine the "optimal purification" of this radiation beyond $\mathcal C$ 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 re-opening it and performing further manipulations.

• The paper demonstrates that optimal purification protocols can significantly reduce decoherence in quantum superpositions near black holes.
• It employs a mode decomposition of the Klein-Gordon equation in Rindler and black hole spacetimes to derive precise energy minimization strategies.
• The research outlines actionable protocols for experimentalists like Alice to manipulate radiation and preserve quantum coherence amid gravitational effects.

Minimizing Decoherence Induced by Black Holes

This paper addresses the issue of decoherence in quantum systems caused by black holes, exploring how an experimentalist can minimize such effects. The primary focus is on a quantum system in the vicinity of a black hole's event horizon and how emitted radiation affects the system's coherence. The research is contextualized within the framework of quantum mechanics, specifically dealing with superpositions and entanglement with the quantum fields.

The main proposition is centered around "Alice," a hypothetical experimentalist who creates quantum superpositions near a black hole. Prior research has demonstrated that soft radiation (photons or gravitons) emitted by the superposition into the black hole leads to decoherence over time. A critical question remains: at any specific moment during this process, exactly how much decoherence has occurred and how do observers, say within the black hole, perceive this?

The paper aims to delineate the optimal experimental strategy for Alice to mitigate the decoherence from time $t > t_c$, given a black hole or a similar Killing horizon presence. The key objective is to determine the "optimal purification" of radiation passing through this horizon such that the global state of the radiation maximizes overlap with vacuum states like the Hartle-Hawking or Unruh vacuum. Notably, the research highlights that even post-experimental closure, Alice can act to reduce decoherence by reopening and manipulating the superposition.

A significant component of this research involves solving for classical solutions to the Klein-Gordon equation in a Rindler spacetime and reflecting this understanding onto a black hole spacetime. The paper executes a mode decomposition using the boost Killing frequency and derives solutions to minimize the energy norm of the states involved.

The choice of continuation for the superposition aims at a balance between reflecting the prior radiative states with a modification informed by Rindler thermal factors. Importantly, the research elucidates that a CRT (cross-section reflection) purification reflects radiation about the cross-section of interest and employs a smooth modulation that decays in energy at higher frequencies.

Theoretical implications reach far into the quantum gravity discussions, particularly with significant soft radiation effects representing an interaction point between a quantum field theory and general relativity concepts. The exploration into this area is relevant for understanding quantum superpositions in gravitational contexts and situating experimental practices within feasible limits of coherence preservation.

In sum, this paper advances our theoretical understanding of quantum decoherence in the presence of strong gravitational fields, offering a precise mathematical framework to devise protocols that help in optimizing quantum state preservation near black holes. Future developments may further explore practical methods for implementing similar strategies in experimental quantum systems subjected to gravitational influences, expanding this theoretical work into the domain of applied quantum information science.