Variational approach to relative entropies with an application to QFT

Abstract We define a new divergence of von Neumann algebras using variational expression similar in nature to Kosaki’s formula for Umegaki’s relative entropy. Our satisfies several the usual desirable properties, upper bounds sandwiched Renyi entropy and reduces fidelity limit. As an illustration, we use quantum field theory compute our between vacuum bipartite system “orbifolded”—in sense conditional expectation—system terms Jones index. take opportunity point out entropic certainty relation associated with inclusion factors related This has equivalent formulation error correcting codes.