Probing quantum scrambling and chaos in curved spacetime via Unruh-DeWitt detectors

Abstract

We introduce a local operational protocol for measuring quantum information scrambling in a curved spacetime background. In this framework, two Unruh-DeWitt (UDW) detectors, coupled to a massless conformally coupled scalar field in the Hartle–Hawking vacuum of the non-rotating (2+1)-dimensional Banados–Teitelboim–Zanelli (BTZ) black hole, serve as local probes. Evaluating the detector out-of-time-ordered correlator requires a fourth-order Dyson series expansion. Within the scrambling regime, this correlator exhibits exponential growth with Lyapunov exponent, exactly saturating the Maldacena–Shenker–Stanford bound at the global Hawking temperature. Governed by the black hole surface gravity, the Lyapunov exponent is universal and independent of detector positions, energy gaps, and coupling strengths. Furthermore, the scrambling amplitude shows a monotonic dependence on the radial positions of the detectors, vanishing at the event horizon and increasing outward. Local two-level probes thus witness the maximal chaos of the BTZ geometry without reconstructing the global quantum field state.