Resource theory of non-Gaussian operations

Abstract

Non-Gaussian states and operations are crucial for various continuous-variable quantum information processingtasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussianoperations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operationsas resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotonethat is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussianchannels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show thatthe non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianityof the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operationsinto two classes: (i) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition,and all Gaussian-dilatable non-Gaussian channels; and (ii) the diverging non-Gaussianity class, e.g., the binaryphase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channelsare exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classificationof non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.