Kavli Affiliate: Robert M. Wald
| First 5 Authors: Daine L. Danielson, Jonah Kudler-Flam, Gautam Satishchandran, Robert M. Wald,
| Summary:
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.
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