Schrödinger found that within quantum mechanics certain states do not allow such a decomposition locally.
The generated one-way steering gives a new insight into quantum physics and may open a new field of applications in quantum information.
The steering effect can be described by considering two remote observers, Alice and Bob, who share a bipartite quantum state.
These decompositions can be seen as more precise descriptions of his system.
Indeed, any information that Alice has about the state will give a decomposition into conditional states that are purer than Bob's mixed state. 2 for the case of a Gaussian system and quadrature measurements.