4.4 Article

Entanglement of purification: from spin chains to holography

Journal

JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 1, Pages -

Publisher

SPRINGER
DOI: 10.1007/JHEP01(2018)098

Keywords

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

Funding

  1. Simons Foundation as part of the It From Qubit Collaboration
  2. NSF [PHY1407744, PHY1708139]
  3. National Science Foundation [PHY-1607611]
  4. DOE SciDAC program [FWP 100368 DE-AC02-76SF00515]
  5. Division Of Physics
  6. Direct For Mathematical & Physical Scien [1407744] Funding Source: National Science Foundation

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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.

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