Holographic interpretation of Shannon entropy of coherence of quantum pure states

Abstract

For a quantum pure state in conformal field theory, we generate the Shannon entropy of its coherence, that is, the von Neumann entropy obtained by introducing quantum measurement errors. We give a holographic interpretation of this Shannon entropy, based on Swingle's interpretation of anti-de Sitter space/conformal field theory (AdS/CFT) correspondence in the context of AdS3/CFT2. As a result of this interpretation, we conjecture a differential geometrical formula for the Shannon entropy of the coherence of a quantum pure or purified state in CFT2 at thermal and momentum equilibrium as the sum of the holographic complexity and the abbreviated action, divided by πℏ, in the bulk domain enclosed by the Ryu-Takayanagi curve. This result offers a definition of the action of a bulk model of qubits dual to the boundary CFT2 at this equilibrium.