  We study a class of decoherence process which admits a 3 dimensional
holographic bulk. Starting from a thermo-field double dual to a wormhole, we
prepare another thermo-field double which plays the role of environment. By
allowing the energy flow between the original and environment thermo-field
double, the entanglement of the original thermo-field double eventually
decoheres. We model this decoherence by four-boundary wormhole geometries, and
study the time-evolution of the moduli parameters to see the change of the
entanglement pattern among subsystems. A notable feature of this holographic
decoherence processes is that at the end point of the processes, the
correlations of the original thermo-field double are lost completely both
classically and also quantum mechanically. We also discuss distinguishability
between thermo-field double state and thermo mixed double state, which contains
only classical correlations, and construct a code subspace toy model for that.

High Energy Physics - Theory;General Relativity and Quantum Cosmology