# Coarse graining the phase space of $N$ qubits

## TL;DR

This paper introduces a systematic method to simplify the phase space of large qubit systems by coarse graining, preserving key properties and enabling practical measurement strategies.

## Contribution

It presents a novel geometrical approach to coarse graining of qubit phase space, facilitating analysis and measurement of large quantum systems.

## Key findings

- Produces a reduced-size phase space with key properties intact
- Derives a subset of measurement operators for coarse-grained Wigner functions
- Provides a systematic approach for incomplete measurements in large systems

## Abstract

We develop a systematic coarse graining procedure for systems of $N$ qubits. We exploit the underlying geometrical structures of the associated discrete phase space to produce a coarse-grained version with reduced effective size. Our coarse-grained spaces inherit key properties of the original ones. In particular, our procedure naturally yields a subset of the original measurement operators, which can be used to construct a coarse discrete Wigner function. These operators also constitute a systematic choice of incomplete measurements for the tomographer wishing to probe an intractably large system.