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Full and efficient characterisation of non-Markovian quantum processes


In science, we often want to characterise the processes undergone by a system of interest; this allows us to both identify the underlying physics driving the process and to predict what will happen to the system the next time the process occurs. If the state of the system at any time depends only on the state of the system at the previous time-step and some predetermined rule then these dynamics are characterised with relative ease. For instance, the dynamics of quantum mechanical systems in isolation is described in this way. But, when a quantum system repeatedly interact with an environment, the environment often ’remembers’ information about the system's past. This leads to non-Markovian processes, which depend nontrivially on the state of the system at all times during its evolution and they are not, in general, be easily characterised using conventional techniques. Since the early days of quantum mechanics it has been a challenge to describe non-Markovian processes. Here we will show that using operational tools from quantum information theory we can fully characterise any non-Markovian process. In general the full characterisation is not efficient, as it requires exponentially large number of experiments. To overcome this obstacle we map the full process to a many-body state. We show that this can be achieved by using linear, in the number of time steps, amount of bipartite entanglement. Next, the state can be measured to any desired precision, thus the process can be characterised to any desired precision. Finally, we define a natural measure for the degree of  non-Markovianity.