The context: We are in the solid state. After a photon absortion by a system with a singlet ground state, the system undergoes the spin-conserving fission of one spin singlet exciton into two spin triplet excitons (for context, see The entangled triplet pair state in acene and heteroacene materials). These spin triplet pair propagates in the solid, still entangled. The quantum-computing-related goal of all this operation would be to transfer the entanglement of the two flying qubits to two positions that are fixed in space and are also well protected from decoherence (low-energy excitations of nuclear spins in a paramagnetic ion, for example).
The problem at hand (2), and the question: Eventually, the entanglement between the two triplets is lost, and moreover inevitably the triplets find a way to relax back to the singlet ground state, emitting energy in form of photons. I would like to calculate how these processes are affected by vibrations. I assume the independent relaxation of each of the two triplets can be calculated mostly considering local vibrations, e.g. following a procedure similar to the one we employed here (Determining key local vibrations in the relaxation of molecular spin qubits and single-molecule magnets). Would the calculation of the loss of entanglement be necessarily related to delocalized vibrational modes that simultaneously involve the local environment of both triplets?