TY - JOUR
T1 - Entanglement of purification
T2 - from spin chains to holography
AU - Nguyen, Phuc
AU - Devakul, Trithep
AU - Halbasch, Matthew G.
AU - Zaletel, Michael P.
AU - Swingle, Brian
N1 - Funding Information:
MPZ is particularly indebted to Frank Pollmann, with whom we first considered and implemented the purification disentangling algorithm. BGS acknowledges support from the Simons Foundation as part of the It From Qubit Collaboration. This work is partially supported by NSF grants PHY1407744 and PHY1708139. MPZ acknowledges the hospitality of the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. MPZ and TD were supported by the DOE SciDAC program, FWP 100368 DE-AC02-76SF00515.
Publisher Copyright:
© 2018, The Author(s).
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
AB - 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.
KW - AdS-CFT Correspondence
KW - Gauge-gravity correspondence
KW - Models of Quantum Gravity
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U2 - 10.1007/JHEP01(2018)098
DO - 10.1007/JHEP01(2018)098
M3 - Article
AN - SCOPUS:85041062571
SN - 1126-6708
VL - 2018
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 1
M1 - 98
ER -