Exponential advantages in learning continuous-variable systems

In this work, we study exponential advantages in learning continuous-variable (CV) quantum channels and quantum states. More specifically, we first consider learning properties of quantum channels in CV systems and prove that entangled probes with ancillary quantum memory can provide an exponential advantage over any strategies that do not employ entanglement with ancillary quantum memory for achieving the task, more specifically, learning random displacement channels [1]. Such a scheme only requires Gaussian state preparation and measurement and is thus easily implementable in experiments. Second, we consider learning properties of quantum states in CV systems and prove that entangled measurement between multi-copies of the quantum states provides an exponential advantage over any strategies that do not use entangled measurement [2]. Our results reveal that entangled probes or measurements are key resources for learning CV quantum systems and that quantum memory to utilize them is crucial. We also experimentally demonstrate the exponential quantum advantage for learning CV quantum channels [3]. We expect that the proposed schemes will provide an efficient way to learn CV systems.