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# About Causal Models and Quantum Stochastic Processes: Does Time-Delayed Feedback turn Markovian into non-Markovian Dynamics?

Lecturer:

Dr. Philipp Strasberg

Dates and Time:** Monday, June 20, 10:15 - 11:45 and Friday, June 24, 10:15 - 11:45**

Place:

**ER 164**

Physik-Altbau

TU Berlin

Physik-Altbau

TU Berlin

The answer is: No! No feedback control loop turns a Markovian process into a non-Markovian one. The goal of this lecture will be to understand why that is the case. To do so, we need to talk about classical stochastic processes, and in particular the meaning of the Kolmogorov consistency condition. We will see that it is necessary to overcome this condition to understand feedback control. This leads to the much richer framework of causal models, which are able to distinguish between correlation and causation (which a classical stochastic process cannot). Interestingly, an understanding of classical causal models brings us very close to an understanding of a quantum stochastic process, describing the most general quantum dynamics respecting causality. The second part of the lecture is then devoted to providing an explicit theoretical framework for quantum stochastic processes and to introduce a meaningful operational Markov condition, which shows that feedback control does not change the Markovianity of the process.