Selective quantum state tomography for continuous-variable systems

We present a protocol that allows the estimation of any density matrix element for continuous-variable quantum states, without resorting to the complete reconstruction of the full density matrix. The algorithm adaptatively discretizes the state and then, by resorting to controlled squeezing and translation operations, which are the main requirements for this algorithm, measures the density matrix element value. Furthermore, we show how this method can be used to achieve full quantum state tomography for continuous-variable quantum systems, alongside numerical simulations.