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 AdS${}_3$/CFT${}_2$. 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 CFT${}_2$ at thermal and momentum equilibrium as the sum of the holographic complexity and the abbreviated action, divided by $\pi \hslash$, 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 CFT${}_2$ at this equilibrium.

9+2 pages, revtex, v6: published version, bundled with the addendum

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Cited by in corpus (3)

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