### Abstract

We consider a quantum system AB 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."

Original language | English (US) |
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Article number | 052133 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 90 |

Issue number | 5 |

DOIs | |

State | Published - Nov 17 2014 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*90*(5), [052133]. https://doi.org/10.1103/PhysRevE.90.052133