title: Reconstructing quantum states from local data.
abstract: We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data. We show that unique ground states of local Hamiltonians are exactly reconstructed as the maximal entropy state. More generally, we show that if the state in question is a ground state of a local Hamiltonian with a degenerate space of locally indistinguishable ground states, then the maximal entropy state is close to the ground state projector. We also show that local reconstruction is possible for thermal states of local Hamiltonians. Finally, we discuss a procedure to certify that the reconstructed state is close to the true global state. We call the entropy of our reconstructed maximum entropy state the "reconstruction entropy," and we discuss its relation to emergent geometry in the context of holographic duality.
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Brian
authors.initials: B
authors.lastname: Swingle
authors.affiliation: Perimeter Institute of Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada and Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Isaac H
authors.initials: IH
authors.lastname: Kim