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Submitted by:** | EISERT, Jens
*FU Berlin*
`jenseisert@gmail.com` |

*Quantum field tomography and continuous matrix-product states*

#### A. Steffens, M. Friesdorf, C. Riofrío, R. Hübener, and J. Eisert

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 applied 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. Furthermore, we 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.