Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes

  • Grant N. RemmenEmail author
  • Ning Bao
  • Jason Pollack
Open Access
Regular Article - Theoretical Physics


We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throat separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. This theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.


Classical Theories of Gravity Black Holes Models of Quantum Gravity Gauge-gravity correspondence 


Open Access

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Walter Burke Institute for Theoretical PhysicsCalifornia Institute of TechnologyPasadenaU.S.A.
  2. 2.Institute for Quantum Information and MatterCalifornia Institute of TechnologyPasadenaU.S.A.

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