Covariant Measures of Non-Markovianity in Curved Spacetime

Abstract: Standard measures of quantum non-Markovianity are usually defined in terms of dynamical maps on a preferred time foliation and therefore do not extend straightforwardly to curved spacetimes, where no global time coordinate exists and causal structure is primary. We develop a covariant framework for open quantum dynamics along arbitrary timelike worldlines by building multi-time quantum processes (process tensors) from overlapping causal diamonds. For an Unruh--DeWitt detector weakly coupled to a scalar field in a Hadamard state, we define a foliation-independent measure of non-Markovianity as the operational distance between the physical process tensor and the convex set of Markovian (CP-divisible) processes. Numerical benchmarks in $(1{+}1)$ dimensions compare inertial motion, uniform acceleration, and static and infalling trajectories in Schwarzschild spacetime. Inertial trajectories are found to be almost Markovian, whereas acceleration and curvature generate pronounced long-range temporal correlations and strong non-Markovian behaviour. In Rindler spacetime, acceleration produces horizon-induced memory tails. In Schwarzschild spacetime, near-horizon field correlations cause both static and freely falling observers to experience enhanced memory, which can remain hidden in single-step diagnostics but becomes evident in multi-time protocols and can even be superactivated by combining different time steps. Our results provide, to our knowledge, the first coordinate-independent, operational quantification of quantum memory in relativistic settings. They identify spacetime curvature, horizons, and acceleration as controllable ingredients that can either degrade or be harnessed as resources in relativistic quantum information tasks, including communication and metrology with accelerated detectors and near black holes.