Quantum field tomography

TL;DR

This paper introduces quantum field tomography, a method for reconstructing quantum fields from correlation data using continuous matrix product states and compressed sensing techniques, enabling new insights into quantum systems.

Contribution

It develops a practical reconstruction method for quantum fields based on correlation functions, combining continuous matrix product states with estimation tools like Prony methods.

Findings

Successfully reconstructs quantum states from correlation data.

Demonstrates robustness against noise in the reconstruction process.

Applicable to experimental quantum systems like ultra-cold atoms.

Abstract

We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product states, a complete set of variational states grasping states in quantum field theory. We innovate a practical method, making use of and developing tools in estimation theory used in the context of compressed sensing such as Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum field states based on low-order correlation functions. In the absence of a phase reference, we highlight how specific higher order correlation functions can still be predicted. We exemplify the functioning of the approach by reconstructing randomised continuous matrix product states from their correlation data and study the robustness of the reconstruction for different noise models. We also apply the method to data generated by simulations based on continuous matrix product states and using the time-dependent variational principle. The presented approach is expected to open up a new window into experimentally studying continuous quantum systems, such as encountered in experiments with ultra-cold atoms on top of atom chips. By virtue of the analogy with the input-output formalism in quantum optics, it also allows for studying open quantum systems.