Entanglement entropy between real and virtual particles inϕ4quantum field theory

Abstract

The aim of this work is to compute the entanglement entropy of real and virtual particles by rewriting the generating functional of ϕ 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 lnðm 0 Þ. 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 ϕ 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 an interaction occurs.

Correlations in twisted double-layer graphene with virtual photons in a microcavity

“…It is well known that the vacuum state of a quantum field is highly entangled, which implies that regions that are spacelike separated contain correlations for those observables that depends on the field [1][2][3]. This physical fact has many consequences in different branches of quantum field theory [4][5][6][7][8][9]. In addition, it has been shown that two detectors that remain spacelike separated can interact locally with the vacuum state getting entangled and the harvested correlations approximation to the light-matter interaction when no angular momentum is transferred [19,20].…”

Entanglement harvesting in double-layer graphene by vacuum fluctuations in a microcavity

“…The vacuum state of a free quantum field, contains correlations of different observables in separate region of spacetime, even when those regions are spacelike separated ( [1], [2], [3]). This nonclassical behavior of the vacuum state of the field is a vital concept in phenomena such as quantum collect calling [4], the black hole information loss problem ( [5], [6]) and quantum energy teleportation ( [7], [8] and [9]). These correlations are, in principle, physically accessible because they can be obtained from the field vacuum via quantum particles detectors that couple to it locally ( [10]).…”