Coarse-grained distinguishability of field interactions

TL;DR

This paper investigates how coarse-graining affects the distinguishability of quantum field interactions, providing methods to compute information metrics on Gaussian states and analyzing the Klein-Gordon field.

Contribution

It introduces a way to calculate quantum information metrics on coarse-grained states, focusing on free bosonic systems and their perturbations, including the Klein-Gordon field.

Findings

Metrics become equal at coarse phase-space resolutions.

Computed scale dependence of interaction distinguishability.

Simplified calculations when resolution exceeds Planck's constant.

Abstract

Information-theoretical quantities such as statistical distinguishability typically result from optimisations over all conceivable observables. Physical theories, however, are not generally considered valid for all mathematically allowed measurements. For instance, quantum field theories are not meant to be correct or even consistent at arbitrarily small lengthscales. A general way of limiting such an optimisation to certain observables is to first coarse-grain the states by a quantum channel. We show how to calculate contractive quantum information metrics on coarse-grained equilibrium states of free bosonic systems (Gaussian states), in directions generated by arbitrary perturbations of the Hamiltonian. As an example, we study the Klein-Gordon field. If the phase-space resolution is coarse compared to h-bar, the various metrics become equal and the calculations simplify. In that context, we compute the scale dependence of the distinguishability of the quartic interaction.