Entanglement of purification: from spin chains to holography

By P. Nguyen, Trithep Devakul, Matthew G. Halbasch, M. Zaletel, Brian Swingle. 2017

230 citations recorded by the source corpus.

A bstractPurification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b3d39dbc3837bb4e1356c5ab841467412594a6db

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In Artificial Intelligence

  1. R. Myers
  2. H. Chen

In Atomic and Molecular Physics, and Optics

  1. H. Chen
  2. Joshua Sandor
  3. Dominik Neuenfeld
  4. I. Reyes
  5. R. Myers
  6. T. Takayanagi
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  8. H. Marrochio

In Nuclear and High Energy Physics

  1. Joshua Sandor
  2. Dominik Neuenfeld
  3. I. Reyes
  4. H. Chen
  5. R. Myers
  6. Aninda Sinha
  7. Ling-Yan Hung
  8. M. Smolkin

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