Some Results On Relative Entropy in Quantum Field Theory
Feng Xu
TL;DR
This paper proves the finiteness of mutual information in free fermion quantum field theories and relates relative entropy to conformal net representations, advancing understanding of quantum information measures in QFT.
Contribution
It establishes the finiteness of mutual information in free fermion QFTs and connects relative entropy with conformal net representation indices, extending previous results.
Findings
Mutual information is finite for free fermions in any Minkowski spacetime dimension.
In 2D chiral CFTs, mutual information is finite for a broad class of theories.
A direct relation between relative entropy and conformal net representation index is provided.
Abstract
We prove that the mutual information for vacuum state as defined by Araki is finite for quantum field theory of free fermions on a Minkowski spacetime of any dimension. In the case of two dimensional chiral conformal field theory (CFT) we use our previous results for the free fermions to show that for a large class of chiral CFT the mutual information is finite. We also provide a direct relation between relative entropy and the index of a representation of conformal net.
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