Quantum field tomography

Abstract

We introduce the concept of quantum field tomography, the efficient and\nreliable reconstruction of unknown quantum fields based on data of correlation\nfunctions. At the basis of the analysis is the concept of continuous matrix\nproduct states (cMPS), a complete set of variational states grasping states in\none-dimensional quantum field theory. We innovate a practical method, making\nuse of and developing tools in estimation theory used in the context of\ncompressed sensing such as Prony methods and matrix pencils, allowing us to\nfaithfully reconstruct quantum field states based on low-order correlation\nfunctions. In the absence of a phase reference, we highlight how specific\nhigher order correlation functions can still be predicted. We exemplify the\nfunctioning of the approach by reconstructing randomized cMPS from their\ncorrelation data and study the robustness of the reconstruction for different\nnoise models. Furthermore, we apply the method to data generated by\nsimulations based on cMPS and using the time-dependent variational principle.\nThe presented approach is expected to open up a new window into experimentally\nstudying continuous quantum systems, such as those encountered in experiments\nwith ultra-cold atoms on top of atom chips. By virtue of the analogy with the\ninput–output formalism in quantum optics, it also allows for studying open\nquantum systems.