What does it mean exactly “matter is broken apart”? There are excitations of the quantum fields (electron-positron field, photon field, etc…) that normally evolve according to some time dependent Hamiltonian from one moment to another and constitutes “you”. This Hamiltonian depends on “external world” or on other excitations of the same fields, that are not “you” (e.g. external light waves, gravity, excitations corresponding to something outside of your body). During transportation, the Hamiltonian is just such that that the excitations are transferred from one particular place, to another place (in some coordinate system) while preserving information. If you were not transported, then excitations would be normally transferred to just different distance (in the same coordinate system). As long as quantum information is mostly preserved by the Hamiltonian, then both the transportation and some other evolution that usually called “normal”, preserves the person with his self-identety and memory. But fundamentally I see no fundamental difference between those two Hamiltonians acting on quantum fields according to Schrödinger equation while preserving most of the quantum information over time.