PIRSA:14080007 Scientific Series Condensed Matter

DOI10.48660/14080007

Series: Quantum Matter

Kim, I. (2014). Reconstructing quantum states from local data. Perimeter Institute. https://pirsa.org/14080007

Kim, Isaac. Reconstructing quantum states from local data. Perimeter Institute, Aug. 12, 2014, https://pirsa.org/14080007 

@misc{ pirsa_PIRSA:14080007,
  doi = {10.48660/14080007},
  url = {https://pirsa.org/14080007},
  author = {Kim, Isaac},
  keywords = {Condensed Matter},
  language = {en},
  title = {Reconstructing quantum states from local data},
  publisher = {Perimeter Institute},
  year = {2014},
  month = {aug},
  note = {PIRSA:14080007 see, \url{https://pirsa.org}}
}

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. This is a joint work with Brian Swingle.

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