  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
$\pi\hbar$, 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.
