Fuzzy measurements and coarse graining in quantum many-body systems

TL;DR

This paper introduces a quantum map framework to model fuzzy and coarse-grained measurements in many-body quantum systems, revealing how measurement limitations affect entanglement and information accessibility.

Contribution

It develops a formalism for constructing fuzzy quantum states accounting for measurement imperfections and characterizes the properties and limitations of these maps in many-body systems.

Findings

Volume of accessible states decreases double exponentially with system size

Fuzzy maps are related via partial trace, simplifying analysis

Symmetries and invariants of the fuzzy map are fully characterized

Abstract

Using the quantum map formalism, we provide a framework to construct fuzzy and coarse grained quantum states of many-body systems that account for limitations in the resolution of real measurement devices probing them. The first set of maps handles particle-indexing errors, while the second deals with the effects of detectors that can only resolve a fraction of the system constituents. We apply these maps to a spin-$1/2$ XX-chain obtaining a blurred picture of the entanglement generation and propagation in the system. By construction, both maps are simply related via a partial trace, which allow us to concentrate on the properties of the former. We fully characterize the fuzzy map, identifying its symmetries and invariants spaces. We show that the volume of the tomographically accessible states decreases at a double exponential rate in the number of particles, imposing severe bounds to the ability to read and use information of a many-body quantum system.