Scalable reconstruction of density matrices

TL;DR

This paper introduces a scalable method for reconstructing mixed quantum states approximated by matrix product operators, using only local information, enabling efficient tomography of large one-dimensional quantum systems.

Contribution

The paper presents a new reconstruction scheme for mixed states based on matrix product operators that is scalable and requires only local data, unlike previous methods.

Findings

Successfully applied to simulated data

Validated with experimental ion trap data

Demonstrates efficiency in large systems

Abstract

Recent contributions in the field of quantum state tomography have shown that, despite the exponential growth of Hilbert space with the number of subsystems, tomography of one-dimensional quantum systems may still be performed efficiently by tailored reconstruction schemes. Here, we discuss a scalable method to reconstruct mixed states that are well approximated by matrix product operators. The reconstruction scheme only requires local information about the state, giving rise to a reconstruction technique that is scalable in the system size. It is based on a constructive proof that generic matrix product operators are fully determined by their local reductions. We discuss applications of this scheme for simulated data and experimental data obtained in an ion trap experiment.