Geometric Quantum Information Structure in Quantum Fields and their Lattice Simulation

TL;DR

This paper investigates the decay of entanglement in quantum fields, defining a negativity sphere that characterizes how entanglement diminishes with distance, with implications for quantum field theories and lattice simulations.

Contribution

It introduces a geometric decay constant for entanglement in scalar fields and explores its behavior in lattice models, connecting to quantum chromodynamics and effective field theories.

Findings

Entanglement decays exponentially with distance in scalar fields.

A negativity sphere defines the range of distillable entanglement.

Lattice calculations show how the negativity sphere grows toward the continuum.

Abstract

An upper limit to distillable entanglement between two disconnected regions of massless non-interacting scalar field theory has an exponential decay defined by a geometric decay constant. When regulated at short distances with a spatial lattice, this entanglement abruptly vanishes beyond a dimensionless separation, defining a negativity sphere. In two spatial dimensions, we determine this geometric decay constant between a pair of disks and the growth of the negativity sphere toward the continuum through a series of lattice calculations. Making the connection to quantum field theories in three-spatial dimensions, assuming such quantum information scales appear also in quantum chromodynamics (QCD), a new relative scale may be present in effective field theories describing the low-energy dynamics of nucleons and nuclei. We highlight potential impacts of the distillable entanglement structure on effective field theories, lattice QCD calculations and future quantum simulations.