# Optimal quantum observables

## TL;DR

This paper explores optimal quantum observables (POVMs), providing characterizations for certainty, noise-free measurements, and conditions for informational completeness, along with analysis of joint and sequential measurement strategies.

## Contribution

It offers new characterizations of noise-free and informationally complete quantum observables, including necessary and sufficient conditions, and examines joint and sequential measurement frameworks.

## Key findings

- Characterization of observables with deterministic measurement outcomes.
- Complete criteria for pre-processing and post-processing clean observables.
- Conditions for informational completeness within pure states.

## Abstract

Various forms of optimality for quantum observables described as normalized positive operator valued measures (POVMs) are studied in this paper. We give characterizations for observables that determine the values of the measured quantity with probabilistic certainty or a state of the system before or after the measurement. We investigate observables which are free from noise caused by classical post-processing, mixing, or pre-processing of quantum nature. Especially, a complete characterization of pre-processing and post-processing clean observables is given, and necessary and sufficient conditions are imposed on informationally complete POVMs within the set of pure states. We also discuss joint and sequential measurements of optimal quantum observables.