Entanglement entropy between real and virtual particles in $\phi ^{4}$ quantum field theory

TL;DR

This paper calculates the entanglement entropy between real and virtual particles in $\,\phi^4$ quantum field theory using correlation functions and perturbation expansion, revealing insights into quantum information aspects of field interactions.

Contribution

It introduces a method to compute entanglement entropy in quantum field theory by rewriting the generating functional as quantum states and observables, extending the analysis to all perturbation orders.

Findings

Entanglement entropy behaves as ln(m_0)

Mutual information equals external entropy at first order

Conditional entropies are negative across all m_0 domains

Abstract

The aim of this work is to compute the entanglement entropy of real and virtual particles by rewriting the generating functional of $\phi ^{4}$ theory as a mean value between states and observables defined through the correlation functions. Then the von Neumann definition of entropy can be applied to these quantum states and in particular, for the partial traces taken over the internal or external degrees of freedom. This procedure can be done for each order in the perturbation expansion showing that the entanglement entropy for real and virtual particles behaves as $\ln (m_{0})$. In particular, entanglement entropy is computed at first order for the correlation function of two external points showing that mutual information is identical to the external entropy and that conditional entropies are negative for all the domain of $m_{0}$. In turn, from the definition of the quantum states, it is possible to obtain general relations between total traces between different quantum states of a r theory. Finally, discussion about the possibility of taking partial traces over external degrees of freedom is considered, which implies the introduction of some observables that measure space-time points where interaction occurs.