Optimization of quantum universal detectors

TL;DR

This paper discusses optimizing universal quantum detectors that can measure any operator expectation value using a fixed measurement setup and data processing, focusing on covariant POVMs.

Contribution

It formulates the optimization problem for data processing functions in universal detectors and provides examples for covariant POVMs, especially with SU(d) symmetry.

Findings

Optimization of data processing functions improves measurement efficiency.

Examples provided for covariant POVMs with SU(d) symmetry.

Universal detectors can measure arbitrary operators with a fixed apparatus.

Abstract

The expectation value <O> of an arbitrary operator O can be obtained via a universal measuring apparatus that is independent of O, by changing only the data-processing of the outcomes. Such a ``universal detector'' performs a joint measurement on the system and on a suitable ancilla prepared in a fixed state, and is equivalent to a positive operator valued measure (POVM) for the system that is ``informationally complete''. The data processing functions generally are not unique, and we pose the problem of their optimization, providing some examples for covariant POVM's, in particular for SU(d) covariance group.