Efficient rational agents for quantum tomographies and inferences

Abstract

We will elaborated on correct inferences, or sometimes plausible ones, when inferring quantum states and processes. Making correct inferences can be considered part of being a rational agent, because one way to act rationally is to reason logically to the conclusion that a given action will achieve our objective and then to act on that conclusion. Yet, correct inference is not all of rationality; in some situations, there is no provably correct thing to do, especially in possession of incomplete information and noise data, but something must still be done. The aspects of quantum mechanics are maturing in both theory and experiment and we still need higher-dimensional systems to test them. Here, we will explore procedures to infer unknown mixed states and unknown quantumdynamics, which can be experimentally viable and efficiently processed.The heart of our methods are hierarchies of semi-definite programs and its flexible formulations. We presented numerous schemes to achieve the optimal results in the paradigm of complete and incomplete information. We tested our methods in different experiments, such as quantum optics and nuclear magnetic resonance (NMR) systems and presented the results here.