# Operational framework for quantum measurement simulability

## TL;DR

This paper develops a comprehensive framework for simulating quantum measurements through classical processing, unifying known concepts and introducing new hierarchies of measurement incompatibility and simulability.

## Contribution

It generalizes joint measurability, establishes hierarchies for measurement incompatibility, and characterizes qubit measurements in terms of projective simulability within a resource-theoretic context.

## Key findings

- Derived a hierarchy for measurement incompatibility.
- Connected different types of measurement simulability.
- Characterized qubit measurements that are projective-simulable.

## Abstract

We introduce a framework for simulating quantum measurements based on classical processing of a set of accessible measurements. Well-known concepts such as joint measurability and projective simulability naturally emerge as particular cases of our framework, but our study also leads to novel results and questions. First, a generalisation of joint measurability is derived, which yields a hierarchy for the incompatibility of sets of measurements. A similar hierarchy is defined based on the number of outcomes used to perform the simulation of a given measurement. This general approach also allows us to identify connections between different types of simulability and, in particular, we characterise the qubit measurements that are projective-simulable in terms of joint measurability. Finally, we discuss how our framework can be interpreted in the context of resource theories.