Measurement-induced phase transitions in quantum teleportation

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 for large rates, the teleportation can be performed at any moment. These two regimes are separated by a phase transition. In order to analyze Kitaev--Yoshida case, we argue that certain projections can be approximated by low-energy quantum channels, which do not heat the system but qualitatively behave like a real projection. An unusual feature of this measurement-induced phase transition is that it can be diagnosed by an observable linear in the density matrix.