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Measurementinduced phase transition in teleportation and wormholes
by Alexey Milekhin, Fedor K. Popov
Submission summary
Authors (as registered SciPost users):  Alexey Milekhin 
Submission information  

Preprint Link:  scipost_202405_00016v1 (pdf) 
Date accepted:  20240603 
Date submitted:  20240514 00:33 
Submitted by:  Milekhin, Alexey 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We demonstrate that some quantum teleportation protocols exhibit measurement induced phase transitions in SachdevYeKitaev model. Namely, KitaevYoshida and GaoJafferisWall protocols have a phase transition if we apply them at a large projection rate or at a large coupling rate respectively. It is wellknown that at small rates they allow teleportation to happen only within a small timewindow. 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 JackiwTeitelboim gravity these phase transitions correspond to the formation of an eternal traversable wormhole. In the KitaevYoshida case this novel type of wormhole is supported by continuous projections.
Author indications on fulfilling journal expectations
 Provide a novel and synergetic link between different research areas.
 Open a new pathway in an existing or a new research direction, with clear potential for multipronged followup work
 Detail a groundbreaking theoretical/experimental/computational discovery
 Present a breakthrough on a previouslyidentified and longstanding research stumbling block
Author comments upon resubmission
First of all, we thank the reviewers for their encouraging and detailed comments. We sincerely apologize for a long delay in our response. New text in the draft in marked in blue (for the editorial team: \new{} command in latex) Also we fixed a number of typos/grammatical mistakes (not marked).
Let us now address the specific questions. Most of these replies are reflected in the manuscript.
Both reviewer asked about the absence of revivals for the KY case:
We believe KY has revivals as well. Because of the decoherence coming from measurements they are damped with time, unlike the MQ case. Their presence can be inferred from the analytical approximation (4.30) in the new version of the paper. Basically, the KY wormhole solution is similar to the standard MQ wormhole solution except that the length $e^{\phi_*}$ is complex. Hence the twopoint function
$$ 1/cos( e^{\phi_*} (t_2  t_1))^{2\Delta} $$not just oscillates, but is damped as well. In the previous version we did not study the numerical evolution for large enough times to see the revivals.
Reviewer 1:
“exponentially many measurements.” Exponentially many in what? This sentence is not clear to me. The better way to phrase this is exponentially many samples. The evolution with postselection means that after performing a measurement, a sample with undesired measurement outcome is completely discarded. So, if the desired outcome has probability $p$, then simulating $t$ timesteps will roughly require $1/p^t$ samples.
On page 4, it would be good to clarify what you mean by “it requires a finite \mu coupling.” Does this mean the effect can’t be seen in > perturbation theory in \mu? The statement we are making is that for a fixed initial state the wormhole becomes eternally traversable only if \mu is large enough. In the paper we find the corresponding critical value analytically as a function of temperature  eq. (3.13) and below. Equations are simple enough to have an exact solution for any \mu. We believe the transition to an eternal wormhole cannot be seen in the perturbation theory in \mu because above the critical \mu the classical solution completely changes its behavior. The equations can be mapped to a classical particle moving in a potential. If \mu is large enough the particle trajectory becomes trapped rather than running away to infinity. Such qualitative change of behavior cannot be treated as a small perturbation.
Around equations 2.72.10 it isn’t clear what the authors mean by the “plus and minus parts,” and when they should be expected to “cancel out.” We added further explanations there. "Plus and minus" parts are literary forward $e^{i H u}$ and backward $e^{i H u}$ time evolution operators in the Heisenbergevolved density matrix $e^{i H u} \rho e^{+ i H u}$.
Reviewer 2:
Section 3.1 contains the review of the MaldacenaQi solution. In principle, their equations are valid even for timedependent \mu, but they never studied them in this regime. Our contribution is Section 3.2, where we solve them after the \mu coupling is suddenly turned on. We have also added the clarification regarding finite \mu coupling.
Dynamics with postselection is somewhat acausal: the system is conditioned to be in a certain state at t=0. Hence, the corresponding saddlepoint in the path integral is modified both after and \textit{before} the projection. After a single projection the solution is the standard thermal solution  eq. (4.18). The projection, unsurprisingly, raises the temperature (since \tilde{\alpha} > \alpha). Before the projection the solution is given by (4.13). In the leading order correction coming from the projection strength $\kappa$ is purely complex, this is why it is hard to interpret it.
Is it straightforward to compare this to the MQ timereversed problem The reverse MQ problem was studied in the original MQ paper. There nothing interesting happens: turning off \mu always leads to the standard TFD solution.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)