ER=EPR, GHZ, and the consistency of quantum measurements

Abstract

This paper illustrates various aspects of the ER=EPR conjecture. It begins with a brief heuristic argument, using the Ryu-Takayanagi correspondence, for why entanglement between black holes implies the existence of Einstein-Rosen bridges.The main part of the paper addresses a fundamental question: Is ER=EPR consistent with the standard postulates of quantum mechanics? Naively it seems to lead to an inconsistency between observations made on entangled systems by different observers. The resolution of the paradox lies in the properties of multiple black holes, entangled in the Greenberger-Horne-Zeilinger pattern.The last part of the paper is about entanglement as a resource for quantum communication. ER=EPR provides a way to visualize protocols like quantum teleportation. In some sense teleportation takes place through the wormhole, but as usual, classical communication is necessary to complete the protocol.

EPR pairs, local projections and quantum teleportation in holography

“…This leads to the final expression: 12) which agrees with the previous CFT result (2.6) up to the finite constant contribution γ b . The finite constant, which is essentially the boundary entropy, is related to the tension T in (4.9).…”

“…12 Note that in our holographic computations we always set the tension parameter T in (4.9) to zero. However, since we are interested in a local projection which minimize S Π B A we need to take a smallest possible value of T , which is related to the smallest value of boundary entropy as found in [34,35] and thus depends on the details of holographic CFT.…”

“…A particular example of such a state is given in terms of a boundary state (or so called Cardy state) |B as follows: 12) where p is a small parameter which correspond to the UV cut off (i.e. lattice spacing) as the norm of a boundary state is divergent.…”

“…the lower half parts) in figure 19. The above holographic model of quantum teleportation is closely related to the one by Susskind [12,13], where we start with three copies of CFTs dual to three asymptotic regions of two AdS black holes. Both share the crucial property that the information is teleported through the Einstein-Rosen bridge.…”

“…The holographic principle [1][2][3], especially the AdS/CFT [4], relates the structures of gravitational spacetimes to those of quantum entanglement as in [5][6][7][8][9][10][11][12][13]. This motivates us to study gravitational counterparts of quantum information theoretic properties.…”