How to Minimize the Decoherence Caused by Black Holes

TL;DR

This paper develops an optimal protocol for an experimenter near a black hole to minimize quantum superposition decoherence caused by entanglement with Hawking radiation, revealing complex entanglement structures and potential decoherence mitigation strategies.

Contribution

It introduces a method to determine the optimal quantum purification of radiation to reduce decoherence in black hole environments, considering the intricate vacuum entanglement structure.

Findings

Optimal purification maximizes quantum fidelity with the vacuum state.

Re-opening and manipulating superpositions can reduce decoherence.

Entanglement structure of the quantum field vacuum is highly nontrivial.

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.