Professor Paolo Solinas

Quasi-probabilities in quantum mechanics: fundamental ideas and applications

In addition to the usual projective measurements, quantum mechanics allows for alternative ways to extract information from a quantum system. Some of these lead to a quasi-probability distribution for the observable measured which are not positively defined. In analogy with the Wigner quasi-probability distribution, the presence of negative regions in the distribution can be used to spot pure quantum behaviors of the system or the dynamics. I will present a particular scheme, called quantum non-demolition, where quasi-probability distribution arises naturally. It exploits an additional quantum detector coupled to the system to be measured which allows us to gain important information about the wave-function of the system. I will discuss the connection with the violation of the Leggett-Garg inequalities, and how this approach identifies pure quantum effects and quantum-to-classical transition due to the interaction with an environment. I will discuss what are the advantages and disadvantages of this approach with some practical examples: the measure of the work done on a quantum system driven by an external field and the calculation of the derivative of a quantum operator.