Mutual Information and Relative Entropy of Sequential Effect Algebras

Jiamei Wang, Xiaomin Gao, Minhyung Cho

Jiamei Wang, Li Jun, Cho Minhyung

Wang Jia-Mei, Junde Wu, Cho Minhyung

In this paper, we introduce and investigate the mutual information and relative entropy on the sequential effect algebra, we also give a comparison of these mutual information and relative entropy with the classical ones by the venn diagrams. Finally, a nice example shows that the entropies of sequential effect algebra depend extremely on the order of its sequential product.

Jonah Kudler-Flam

We prove an entropic $c$-theorem in two dimensions by constructing a $c$-function from the mutual information between spacelike separated wedges, defined through the relative entropy. The proof follows Casini and Huerta's, with strong subadditivity of entanglement entropy replaced by increasing differences of the mutual information, which we prove directly in the continuum from the split property and standard properties of relative entropy. The benefit of relative entropy is that every quantity we use is finite and no cutoff ever needs to be introduced. The assumptions of the theorem are only the standard axioms of algebraic quantum field theory, the split property with finite mutual information across a gap (both implied by modular $p$-nuclearity), and a finite ultraviolet bound on the resulting $c$-functions. We also note that, formally, the $c$-function is proportional to the minimal averaged null energy of a state that reproduces the vacuum correlations between the two wedges.

Matthew Kreitzer

Jia Wang

In this paper,we introduce and investigate the mutual information and relative entropy on the sequential effect algebra,we also give a comparison of these mutual information and relative entropy with the classical ones by the venn diagrams.Finally,a nice example shows that the entropies of sequential effect algebra depend extremely on the order of its sequential product.