Qubits on the horizon: decoherence and thermalization near black holes

We examine the late-time evolution of a qubit (or Unruh-De Witt detector) that hovers very near to the event horizon of a Schwarzschild black hole, while interacting with a free quantum scalar field. The calculation is carried out perturbatively in the dimensionless qubit/field coupling g, but rather than computing the qubit excitation rate due to field interactions (as is often done), we instead use Open EFT techniques to compute the late-time evolution to all orders in g(2)t/r(s) (while neglecting order g(4)t/r(s) effects) where r(s) = 2GM is the Schwarzschild radius. We show that for qubits sufficiently close to the horizon the late-time evolution takes a simple universal form that depends only on the near-horizon geometry, assuming only that the quantum field is prepared in a Hadamard-type state (such as the Hartle-Hawking or Unruh vacua). When the redshifted energy difference, omega (infinity), between the two qubit states (as measured by a distant observer looking at the detector) satisfies omega (infinity)r(s) << 1 this universal evolution becomes Markovian and describes an exponential approach to equilibrium with the Hawking radiation, with the off-diagonal and diagonal components of the qubit density matrix relaxing to equilibrium with different characteristic times, both of order r(s)/g(2).

Automated summary

The study examines the late-time evolution of a qubit near the event horizon of a Schwarzschild black hole interacting with a free quantum scalar field. It is found that for qubits sufficiently close to the horizon, the late-time evolution takes a simple universal form dependent only on the near-horizon geometry.