Measurement-induced phase transition in teleportation and wormholes

We demonstrate that some quantum teleportation protocols exhibit measurement induced phase transitions in Sachdev–Ye–Kitaev model. Namely, Kitaev–Yoshida and Gao–Jafferis–Wall protocols have a phase transition if we apply them at a large projection rate or at a large coupling rate respectively. It is well-known that at small rates they allow teleportation to happen only within a small time-window. We show that at large rates, the system goes into a new steady state, where the teleportation can be performed at any moment. In dual Jackiw–Teitelboim gravity these phase transitions correspond to the formation of an eternal traversable wormhole. In the Kitaev–Yoshida case this novel type of wormhole is supported by continuous projections.