Optimizing quantum process tomography with unitary 2-designs

TL;DR

This paper demonstrates that weighted unitary 2-designs provide optimal measurement strategies for ancilla-assisted quantum process tomography, especially for unital channels, using minimal orthogonal measurement sets.

Contribution

It introduces the use of weighted unitary 2-designs as optimal measurement schemes for quantum process tomography, including for general quantum channels.

Findings

Weighted unitary 2-designs define optimal measurements for unital channels.

Complete sets of mutually unbiased unitary-operator bases are examples of these designs.

Minimal series of orthogonal measurements can be specified for process tomography.

Abstract

We show that weighted unitary 2-designs define optimal measurements on the system-ancilla output state for ancilla-assisted process tomography of unital quantum channels. Examples include complete sets of mutually unbiased unitary-operator bases. Each of these specifies a minimal series of optimal orthogonal measurements. General quantum channels are also considered.