In 1932 Erwin Schrödinger pointed out a curious analogy between classical diffusion and the probabilistic formalism of quantum physics.

This analogy is further deepened, when post-selection of measurement data is considered. While classical diffusion (Wiener Process) is an irreversible physical process, with a clearly defined arrow of time, post-selection allows one to reveal a time-symmetric level (Bernstein Process) hidden in it.

Now, application of post-selection is becoming more and more important in both theoretical and experimental research in quantum physics. This is particularly important when studying entangled quantum systems, or performing experiments using the so-called weak measurement technique.

While the implications of the classical–quantum analogy discovered by Schrödinger, and further elaborated e.g. by Zambrini et al., are still somewhat unclear, there is hope that studying this property will shed light on many questions in Foundations of Physics, especially the role 
of time in physics, and many of the so-called ‘mysteries’ of quantum physics.

Further, a deepened understanding of this connection may also shed more light on the possibilities of practical applications in fields such as Quantum Computing & Quantum Cryptography.