Theory Seminar: Quantum learning theory with bosonic systems

Francesco Mele
Scuola Normale Superiore di Pisa
QIC Seminar, at the Seminar Room
Monday, July 20, 11:30 CET 

The talk will be based on our recent works at the intersection between two important fields of quantum information: quantum learning theory and continuous-variable (CV) systems. Quantum learning theory addresses the question of how to extract classical information from quantum systems as efficiently as possible. CV systems are ubiquitous in nature and in quantum technologies, as they model bosonic systems and quantum optical platforms. The intersection between these two fields raises many interesting questions, some of which are addressed in our recent works. The first natural question is: what are the ultimate achievable performances of tomography for CV systems? We answer this question by establishing the optimal sample complexity of tomography of Gaussian states (efficient task) and non-Gaussian states (extremely inefficient task). Other natural questions explored in our recent works include: How the sample complexity of CV tomography grows with the degree of non-Gaussianity of the unknown state? How can we efficiently learn Gaussian processes? And how can we efficiently test whether an unknown CV state is Gaussian or far from the set of Gaussian states? As a by-product of our analysis, we establish mathematical tools which may be of independent interest, including: (i) bounds on the trace distance between CV states in terms of their covariance matrices, and (ii) a Gaussian version of the recently introduced random purification channel.