# Quantum process tomography via optimal design of experiments

## TL;DR

This paper formulates quantum process tomography as a design of experiments problem, exploring how classical statistical methods can be adapted to quantum estimation, highlighting unique quantum features and challenges.

## Contribution

It introduces a proper formulation of quantum process tomography within the DoE framework, addressing quantum-specific issues like nuisance parameters.

## Key findings

- Illustrates the link between quantum process tomography and classical DoE
- Highlights quantum-specific features absent in classical settings
- Provides examples demonstrating the application of DoE to quantum problems

## Abstract

Quantum process tomography --- a primitive in many quantum information processing tasks --- can be cast within the framework of the theory of design of experiment (DoE), a branch of classical statistics that deals with the relationship between inputs and outputs of an experimental setup. Such a link potentially gives access to the many ideas of the rich subject of classical DoE for use in quantum problems. The classical techniques from DoE cannot, however, be directly applied to the quantum process tomography due to the basic structural differences between the classical and quantum estimation problems. Here, we properly formulate quantum process tomography as a DoE problem, and examine several examples to illustrate the link and the methods. In particular, we discuss the common issue of nuisance parameters, and point out interesting features in the quantum problem absent in the usual classical setting.