Fig. 2: Efficiency of quantum state tomography of CV systems.
From: Learning quantum states of continuous-variable systems
a, We establish fundamental bounds on the resources required for quantum-state tomography of CV kth-moment-constrained quantum states, highlighting the pronounced inefficiency of any strategy aiming to solve this task. b, Our results encompass any possible strategy, including those using only homodyne and heterodyne measurements, as well as other experimentally feasible operations in photonic platforms, and even general measurements. This means, independently of the techniques used, the tomography of CV states is impractical. c, We identify three key results, labelled facts A–C. The implication is that the resources needed for tomography exhibit strong dependence on the desired accuracy, scaling as ~ε−2n/k.
