Fuzzy measurements and coarse graining in quantum many-body systems

Using the quantum map formalism, we provide a framework to construct fuzzy and coarse-grained quantum maps 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-$1/2 \mathit{XX}$ 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 allows us to concentrate on the properties of the former. We fully characterize the fuzzy map, identifying its symmetries and invariant 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 on the ability to read and use information of a many-body quantum system.