  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.
