Continuous matrix product state tomography of quantum transport experiments

TL;DR

This paper develops a continuous matrix product state (cMPS) tomography method for quantum transport experiments, enabling the reconstruction of complex quantum correlations and waiting time distributions from experimental data.

Contribution

It extends cMPS tomography to include low-order counting probabilities and applies it to fermionic quantum transport, revealing new measurable quantities.

Findings

Reconstruction schemes now include low-order counting probabilities.

The method can access high-order correlations and waiting time distributions.

Demonstrated with actual experimental data.

Abstract

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 condensed-matter 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 the tomographic possibilities of cMPS by showing that reconstruction schemes do not need to be based on low-order correlation functions only, but also on low-order counting probabilities. We show that fermionic quantum transport settings can be formulated within the cMPS framework. This allows us to present a reconstruction scheme based on the measurement of low-order correlation functions that provides access to quantities that are not directly measurable with present technology. Emblematic examples are high-order correlations functions and waiting times distributions (WTD). The latter are of particular interest since they offer insights into short-time scale physics. We demonstrate the functioning of the method with actual data, opening up the way to accessing WTD within the quantum regime.