Coarse-grained distinguishability of field interactions

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.

References in corpus (2)

• Quantum fidelity for arbitrary Gaussian states
• Gravity Dual of Quantum Information Metric

Cited by in corpus (7)

• Nonperturbative renormalization for the neural network-QFT correspondence
• Relevance in the Renormalization Group and in Information Theory
• Field theoretical approach for signal detection in nearly continuous positive spectra II: Tensorial data
• Signal detection in nearly continuous spectra and symmetry breaking
• Field theoretical approach for signal detection in nearly continuous positive spectra I: Matricial data
• Inferring relevant features: from QFT to PCA
• Functional Renormalization Group Approach for Signal Detection