Search for classical subsystems in quantum worlds

Decoherence and einselection explain many features of the emergence classical world from an underlying quantum theory. However, the theory assumes a particular factorization of the global Hilbert space into constituent system and environment subsystems. In this work, given a fixed Hamiltonian we show that there can exist several factorizations (or tensor product structures) of a global Hilbert space that admit a quasiclassical description of subsystems in the sense that certain states (the “pointer states”) are robust to entanglement. We derive several analytical forms that the Hamiltonian may take in such factorizations, each with its unique set of features. Our approach enables us to derive the division into quasiclassical subsystems and demonstrates that decohering subsystems do not necessarily align with our classical notion of locality. These results have interesting ramifications for the interpretation of quantum mechanics and, more practically, may be useful in algorithmically characterizing decoherence free subspaces.