The Spatiotemporal Doubled‐Density Operator: A Unified Framework for Analyzing Spatial and Temporal Quantum Processes

Abstract

AbstractThe measurement statistics for spatial and temporal quantum processes are produced through distinct mechanisms. Measurements that are space‐like separated exhibit non‐signaling behavior. However, time‐like separated measurements can only result in one‐way non‐signaling, as the past is independent of the future, but the opposite is not true. This work presents the doubled‐density operator as a comprehensive framework for studying quantum processes in space‐time. It effectively captures all the physical information of the process, with the measurement and Born rule showing uniformity for both spatial and temporal cases. It is demonstrated that the equal‐time density operator can be derived by performing a partial trace operation on the doubled‐density operator. Furthermore, the temporality of the quantum process can be detected by conducting a partial trace operation on either the left or right half of the doubled‐density operator.