title: Eigenstate thermalization and representative states on subsystems.
abstract: We consider a quantum system A∪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."
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Vedika
authors.initials: V
authors.lastname: Khemani
authors.affiliation: Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Anushya
authors.initials: A
authors.lastname: Chandran
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Hyungwon
authors.initials: H
authors.lastname: Kim
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: S L
authors.initials: SL
authors.lastname: Sondhi