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Title:
Locally indistinguishable states and long-range entanglement
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Abstract:
We will discuss three aspects of locally indistinguishable states, in an order of increasing generality. First, we start with example Hamiltonians arising from quantum error correcting codes. Basics of quantum codes will be reviewed, and a commutative-algebraic formulation will be introduced, from which many examples can be constructed. Second, we view the phase of matter as a equivalence class of many-body states under local unitary transformations, and derive some bulk invariants of the class. The invariants are so sharp that we can give a lower bound on the depth of local quantum circuits that generate the state. Lastly, we will employ quantum Shannon theory to address some properties of locally indistinguishable states. This is a very general form of quantum error correction on lattices, and avoids Hamiltonians entirely.
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