Entanglement of purification: from spin chains to holography

Phuc Nguyen, Trithep Devakul, Matthew G. Halbasch, Michael P. Zaletel, Brian Swingle

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150 Scopus citations


Purification 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.

Original languageEnglish (US)
Article number98
JournalJournal of High Energy Physics
Issue number1
StatePublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • AdS-CFT Correspondence
  • Gauge-gravity correspondence
  • Models of Quantum Gravity


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