Perhaps the following theoretical idea related to how cold fusion may occur
is highly naive, but since I could not find any documentation discussing this the
only way to find out is to bring it up.
The question is whether low-temperature nuclear fusion could be
facilitated by quantum-entanglement of two deuterium nuclei with
the external degrees of freedom (eg the phonons in a metal-lattice
in which the D-nuclei are dissolved).
The idea is that if two D-nuclei are entangled with independent exterior degrees
of freedom then the density matrix describing the subsystem of two D-nuclei
can be diagonal (this happens when we take the trace over all states which are entangled with the two D-nuclei) and therefore the interaction hamiltonian vanishes even when the two
nuclei have overlapping wave-functions in space and time. In the case where
the two states described by the density matrix are mutually exclusive in a classical
sense (e.g., the states corresponding to finding the first D-nucleus or the second
D-nucleus in the same location) then the diagonal elements of the density
matrix are normally interpreted as the probability of finding the first or
the second D-nucleus if a measurement where performed (but not both).
Now the vanishing of an interaction Hamiltonian suggests that the electrostatic repulsion between two D-nuclei could be temporarily neutralized, along with the weak and the strong interactions.
For two decohered nuclei at the same location it would take recoherence (through alignment of the exterior degrees of freedom with which the two nuclei are entangled) to restore the interactions. If the two nuclei recohere with sufficient overlap so that the strong attraction exceeds the electrostatic repulsion then fusion may occur.
In a nutshell, the idea is whether decoherence followed by the spatial overlapping of the wave-functions of two D-nuclei followed by recoherence
could produce nuclear fusion at low temperatures.