Covariant Measures of Non-Markovianity in Curved Spacetime Define Operational Distance Between Processes for Unruh, DeWitt Detectors

The challenge of quantifying how systems lose memory of their initial state, known as non-Markovianity, becomes particularly complex in the warped spacetime around massive objects, where conventional measurement techniques fail. Tushar Waghmare, from the Indian Institute of Technology Kharagpur, and colleagues now present a new framework for measuring this loss of memory in curved spacetime, independent of any specific coordinate system. The team develops a method that constructs a comprehensive picture of how information evolves along any path through spacetime, revealing that acceleration and curvature dramatically increase long-range temporal correlations and strong non-Markovian behaviour. This research delivers, to the best of current knowledge, the first coordinate-independent quantification of memory in relativistic settings, identifying spacetime curvature, horizons, and acceleration as controllable factors that can either hinder or enhance information processing in extreme environments like those near black holes.

Hawking-Unruh Effect and Quantum Vacuum Thermalisation

This research explores the interplay between quantum field theory in curved spacetime and quantum information, focusing on the Hawking-Unruh effect, which predicts that an accelerating observer perceives a thermal bath of particles, even in a vacuum. Understanding this effect requires careful consideration of the quantum vacuum state, altered by spacetime curvature, and scientists employ the Hadamard condition to ensure well-behaved quantum fields in curved spacetime. The work also draws on concepts from quantum information theory, including quantum channels and quantum supermaps, to model how quantum information is transmitted and affected by external influences. Researchers use tools like conditional mutual information and semidefinite programming to quantify correlations and optimize quantum information protocols, providing a rigorous framework for analysing complex quantum phenomena.

Key to this analysis is the Unruh-DeWitt detector, a theoretical device used to detect the thermal particles predicted by the Unruh effect. Scientists investigate variations of this detector in different spacetime geometries, employing Hadamard renormalization to remove divergences from calculations, and utilise the Choi-Jamiołkowski state and completely positive maps to characterise quantum processes. Concepts like strong subadditivity and quantum causal modelling further refine the understanding of quantum entropy and causality.

Spacetime Curvature Induces Quantum Memory Effects

This work introduces a new framework for quantifying quantum non-Markovianity, a measure of how a system’s past influences its future, along any path through curved spacetime. By constructing process tensors from overlapping regions of spacetime, researchers defined non-Markovianity as the distance between a system’s actual behaviour and what would be expected from a memoryless process, yielding a measure independent of specific coordinate choices. The analysis demonstrates that acceleration and spacetime curvature genuinely create quantum memory, inducing long-range temporal correlations that can be harnessed for information processing. Specifically, the team found that uniformly accelerated motion in flat space and the presence of horizons, such as those around black holes, enhance these correlations, even “superactivating” memory in certain multi-probe settings.

The results establish a connection between spacetime geometry and the potential for quantum information tasks, like improved clocks and communication with accelerated observers. The authors acknowledge that their current analysis relies on approximations and is limited to massless particles, with future research focused on extending the framework to more complex scenarios, incorporating spin or gauge fields, and exploring dynamic spacetimes, as well as developing curvature-aware error correction protocols and investigating multi-detector networks with entangled probes. Ultimately, this work contributes to a growing understanding of how spacetime itself can participate in quantum processing, blurring the lines between quantum information and geometry.