Ground state nature and nonlinear squeezing of Gottesman-Kitaev-Preskill states

The main bottleneck for universal quantum computation with traveling light is the preparation of Gottesman-Kitaev-Preskill states of sufficient quality. This is an extremely challenging task, experimental as well as theoretical, also because there is currently no single easily computable measure of quality for these states. We introduce such measure, GKP squeezing, and show how it is related to the current ways of characterizing the states. The measure is easy to compute and can be easily employed in state preparation as well as verification of experimental results.