Unique Quantum Paths by Continuous Diagonalization of the Density Operator

In this short note we show that for a Markovian open quantum system it is always possible to construct a unique set of perfectly consistent Schmidt paths, supporting quasi-classicality. Our Schmidt process, elaborated several years ago, is the $\mathrm{\Delta }t\to 0$ limit of the Schmidt chain constructed very recently by Paz and Zurek.