Quantum physics vs Probability theory

[Stephen Tashi]

Of course, QT-time evolution is not equivalent to a stochastic Markov process. Why should it be?

The question of whether a phenomena is or isn't a Markov process isn't well posed until we specify the definition of "state". One thought is that the claim that QM predictions can't be modeled by a Markov process means that they cannot be modeled a Markov process using the QM definition of state. (Given absolute freedom to define "state" as one wishes, how could we show that no Markov model of a phenomena exists?)

However, if the state of a physical system evolves deterministically, there there is no probability involved in the model unless we regard it as a trivial Markov process where the state at time t transitions to the state at time t + dt with probability 1. However, isn't the claim that the QM model is not a Markov process more than an objection to such triviality?

What definition of "state of a process" is being used when we say that the results of QM cannot be modeled by a Markov process?