Are entangled particles connected by wormholes? Evidence for the ER=EPR conjecture from entropy inequalities

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 Einstein-Rosen (ER) bridges (or wormholes) connecting them. We show that the geometrical entropy of classical ER bridges satisfies the subadditivity, triangle, strong subadditivity, and Cadney-Linden-Winter 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 |GHZ4