Are entangled particles connected by wormholes? Evidence for the ER =EPR conjecture from entropy inequalities
Abstract
If spacetime is built out of quantum bits, does the shape of space depend on how the bits are entangled? The ER =EPR conjecture relates the entanglement entropy of a collection of black holes to the cross sectional area of EinsteinRosen (ER) bridges (or wormholes) connecting them. We show that the geometrical entropy of classical ER bridges satisfies the subadditivity, triangle, strong subadditivity, and CadneyLindenWinter inequalities. These are nontrivial properties of entanglement entropy, so this is evidence for ER =EPR. We further show that the entanglement entropy associated with classical ER bridges has nonpositive tripartite information. This is not a property of entanglement entropy, in general. For example, the entangled four qubit pure state GHZ_{4}⟩=(0000⟩+1111⟩)/√2 has positive tripartite information, so this state cannot be described by a classical ER bridge. Large black holes with massive amounts of entanglement between them can fail to have a classical ER bridge if they are built out of GHZ_{4}⟩ states. States with nonpositive tripartite information are called monogamous. We conclude that classical ER bridges require monogamous EPR correlations.
 Publication:

Physical Review D
 Pub Date:
 March 2014
 DOI:
 10.1103/PhysRevD.89.066001
 arXiv:
 arXiv:1308.0289
 Bibcode:
 2014PhRvD..89f6001G
 Keywords:

 11.25.Tq;
 04.60.m;
 04.70.Dy;
 Gauge/string duality;
 Quantum gravity;
 Quantum aspects of black holes evaporation thermodynamics;
 High Energy Physics  Theory;
 Astrophysics  Cosmology and Extragalactic Astrophysics
 EPrint:
 11 pages, 4 figures