Środowiskowe Seminarium z Informacji i Technologii Kwantowych

In science, we often want to characterise processesundergone by a system; this allows us to both identify the underlyingphysics and to predict the future of the system. If the state of thesystem at any time depends only on the state of the system at theprevious time-step and some predetermined rule then these dynamics arecharacterised with relative ease. For instance, the dynamics ofquantum mechanical systems in isolation is described in this way. But,when a quantum system repeatedly interact with an environment, theenvironment often ’remembers’ information about the system's past.This leads to non-Markovian processes, which depend nontrivially onthe state of the system at all times during its evolution and they arenot, in general, be easily characterised using conventionaltechniques. Since the early days of quantum mechanics it has been achallenge to describe non-Markovian processes. Here we will show thatusing operational tools from quantum information theory we can fullycharacterise any non-Markovian process. In general the fullcharacterisation is not efficient, as it requires exponentially largenumber of experiments. To overcome this obstacle we map the fullprocess to a many-body state. We show that this can be achieved byusing linear (in the number of time steps) amount of bipartiteentanglement. Next, the state can be measured to any desiredprecision, thus the process can be characterised to any desiredprecision. Finally, we define a natural measure for the degree ofnon-Markovianity.