From Nonlinear Stochastic Differential Equations to Quantum Channels: The Kolmogorov--Lindblad Mapping
The Kolmogorov–Lindblad Mapping (KLM) provides a mathematical link between complex nonlinear stochastic differential equations and quantum channels. It transforms the pathwise probability density of these dynamics into the position diagonal of a trace-one quantum density operator. This allows researchers to derive a Lindblad equation whose diagonal kernel exactly matches the classical Fokker–Planck density, effectively encoding uncertainty about realized stochastic paths.