Holographic measurement and quantum teleportation in the SYK thermofield double

Abstract

According to holography, entanglement is the building block of spacetime; therefore, drastic changes of entanglement will lead to interesting transitions in the dual spacetime. In this paper, we study the effect of projective measurements on the Sachdev-Ye-Kitaev (SYK) model’s thermofield double state, dual to an eternal black hole in Jackiw-Teitelboim (JT) gravity. We calculate the (Renyi-2) mutual information between the two copies of the SYK model upon projective measurement of a subset of fermions in one copy. We propose a dual JT gravity model that can account for the change of entanglement due to measurement, and observe an entanglement wedge phase transition in the von Neumann entropy. The entanglement wedge for the unmeasured side changes from the region outside the horizon to include the entire time reversal invariant slice of the two-sided geometry as the number of measured Majorana fermions increases. Therefore, after the transition, the bulk information stored in the measured subsystem is not entirely lost upon projection in one copy of the SYK model, but rather teleported to the other copy. We further propose a decoding protocol to elucidate the teleportation interpretation, and connect our analysis to the physics of traversable wormholes.