Abstract
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".
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