Informationally Incomplete Quantum Tomography

TL;DR

This paper reviews the challenges of quantum state and process tomography in large Hilbert spaces, emphasizing informationally incomplete methods and maximum-likelihood techniques for resource-efficient quantum characterization.

Contribution

It provides a tutorial overview of informationally incomplete quantum tomography and highlights maximum-likelihood methods as practical tools for quantum state and process estimation.

Findings

Discusses resource limitations in quantum tomography

Introduces maximum-likelihood techniques for incomplete data

Provides educational overview for newcomers to the field

Abstract

In quantum-state tomography on sources with quantum degrees of freedom of large Hilbert spaces, inference of quantum states of light for instance, a complete characterization of the quantum states for these sources is often not feasible owing to limited resources. As such, the concepts of informationally incomplete state estimation becomes important. These concepts are ideal for applications to quantum channel/process tomography, which typically requires a much larger number of measurement settings for a full characterization of a quantum channel. Some key aspects of both quantum-state and quantum-process tomography are arranged together in the form of a tutorial review article that is catered to students and researchers who are new to the field of quantum tomography, with focus on maximum-likelihood related techniques as instructive examples to illustrate these ideas.