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In recent years, a close connection between the description of open quantum systems, the input-output formalism of quantum optics, and continuous matrix product states in quantum field theory has been established. So far, however, this connection has not been extended to the quantum transport context. In this work, we substantially develop further and apply a machinery of continuous matrix product states (cMPS) to perform tomography of transport experiments. We first present an extension of thedoi:10.1088/1367-2630/17/11/113024 fatcat:iswrinuyfvgvlifa2ck5neex7a