Zurek and Schlosshauer do mention the factoring problem - whether it is a problem depends on what interpretation one is using.
Schlosshuaer,
http://arxiv.org/abs/quant-ph/0312059
p8: Also, there exists no general criterion for how the total Hilbert space is to be divided into subsystems, while at the same time much of what is called a property of the system will depend on its correlation with other systems. This problem becomes particularly acute if one would like decoherence not only to motivate explanations for the subjective perception of classicality (as in Zurek’s “existential interpretation,” see Zurek, 1993, 1998, 2003b, and Sec. IV.C below), but moreover to allow for the definition of quasiclassical “macrofacts.” Zurek (1998, p. 1820) admits this severe conceptual difficulty: In particular, one issue which has been often taken for granted is looming big, as a foundation of the whole decoherence program. It is the question of what are the “systems” which play such a crucial role in all the discussions of the emergent classicality. (. . . ) [A] compelling explanation of what are the systems—how to define them given, say, the overall Hamiltonian in some suitably large Hilbert space—would be undoubtedly most useful.
Zurek,
http://arxiv.org/abs/quant-ph/9805065
p2: We can mention two such open issues right away: Both the formulation of the measurement problem and its resolution through the appeal to decoherence require a Universe split into systems. Yet, it is far from clear how one can define systems given an overall Hilbert space “of everything” and the total Hamiltonian.
p22: As noted before, the problem of measurement cannot be even stated without a recognition of the existence of systems. Therefore, our appeal to the same assumption for its resolution is no sin. However, a compelling explanation of what are the systems — how to define them given, say, the overall Hamiltonian in some suitably large Hilbert space — would be undoubtedly most useful.
