Eigenstate Thermalization and Representative States on Subsystems
  We consider a quantum system A U B made up of degrees of freedom that can be partitioned into spatially disjoint regions A and B. When the full system is in a pure state in which regions A and B are entangled, the quantum mechanics of region A described without reference to its complement is traditionally assumed to require a reduced density matrix on A. While this is certainly true as an exact matter, we argue that under many interesting circumstances expectation values of typical operators anywhere inside A can be computed from a suitable pure state on A alone, with a controlled error. We use insights from quantum statistical mechanics - specifically the eigenstate thermalization hypothesis (ETH) - to argue for the existence of such "representative states". 
Vedika Khemani, Anushya Chandran, Hyungwon Kim, S. L. Sondhi
cond-mat.stat-mech quant-ph