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arXiv:1708.09370 · Journal of High Energy Physics

Quantum teleportation through time-shifted AdS wormholes

Rik van Breukelen, Kyriakos Papadodimas

Published Aug 1, 2018• 26 citations
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Abstract

Abstract Based on the work of Gao-Jafferis-Wall and Maldacena-Stanford-Yang, we observe that the time-shifted thermofield states of two entangled CFTs can be made traversable by an appropriate coupling of the two CFTs, or alternatively by the application of a modified quantum teleportation protocol. This provides evidence for the smoothness of the horizon for a large class of entangled states related to the thermofield by time-translations. The smoothness of these states has some relevance for the firewall paradox and the proposal that some observables in quantum gravity may be state-dependent. We notice that quantum teleportation through these entangled states could be used in a laboratory setup to implement a “time-machine”, which allows the observer to travel far in the future.

DOI
10.1007/jhep08(2018)142

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Abstract Based on the work of Gao-Jafferis-Wall and Maldacena-Stanford-Yang, we observe that the time-shifted thermofield states of two entangled CFTs can be made traversable by an appropriate coupling of the two CFTs, or alternatively by the application of a modified quantum teleportation protocol. This provides evidence for the smoothness of the horizon for a large class of entangled states related to the thermofield by time-translations. The smoothness of these states has some relevance for the firewall paradox and the proposal that some observables in quantum gravity may be state-dependent. We notice that quantum teleportation through these entangled states could be used in a laboratory setup to implement a “time-machine”, which allows the observer to travel far in the future.
This work starts by generalizing the traversable wormhole protocol from the thermofield double state black hole to time-shifted thermofield double state black holes and typical pure state black holes. The protocol is dependent on the time-shift and on the state respectively. The traversability of these states is evidence of the smoothness of the black hole horizons of these states. Inspired by these results, we show that the state-dependent construction of the interior of typical state black holes can be simplified using explicit time dependence. This reduces the state dependence to a single parameter.
We study how energy and quantum entanglement are transferred when two identical CFTs are entangled locally. This is probed by considering a local operator insertion in one of the CFTs. When the CFTs have holographic duals via the AdS/CFT correspondence, the transfer happens through an AdS wormhole that allows signal propagation even beyond the horizon from one AdS boundary to the other; we demonstrate this in explicit CFT calculations. We argue that this transmission is possible because the insertion of a local operator is not a unitary process but a regularized version of projection measurement, and that this is interpreted as quantum teleportation. We also find that this leads to a phenomenon opposite to scrambling, where mutual information, instead of being suppressed, gets enhanced by the insertion of a local operator excitation.
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.
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.
Recent works suggest that quantum theory may support a unification of the notions of space and time, thus treating the spatial and temporal quantum correlations equally. Specifically, the partial transposition of the maximally entangled state of two quantum systems at one time exactly matches the temporal quantum correlations of one quantum system that evolves unitary between two distinct moments of time. In this work we consider this equivalence of spatial and temporal quantum correlations in the context of AdS/CFT duality. We show that in the high temperature limit the thermofield double state is equivalent to the temporal quantum correlations of a quantum theory evolving unitary between two times. Thus, on the gravity side, we argue that the temporal correlations correspond to a black hole at one time connected behind the horizon by an Einstein-Rosen bridge to the same black hole at another time. Moreover, we construct the spacetime corresponding to this temporal wormholes and find that the spacetime is consistent with the interior solution of the BTZ black hole. We conclude suggesting that the BTZ interior solution could have an interpretation in the dS/CFT correspondence framework.
The holographic principle and its realization in the AdS/CFT correspondence led to unexpected connections between general relativity and quantum information. This set the stage for studying aspects of quantum gravity models, which are otherwise difficult to access, in table-top quantum-computational experiments. Recent works have designed a special teleportation protocol that realizes a surprising communication phenomenon most naturally explained by the physics of a traversable wormhole. In this work, we have carried out quantum experiments based on this protocol on state-of-the-art quantum computers. The target quantum processing units (QPUs) included the Quantinuum's trapped-ion System Model H1-1 and five IBM superconducting QPUs of various architectures, with public and premium user access. We report the observed teleportation signals from these QPUs with the best one reaching 80% of theoretical predictions. We outline the experimental challenges we have faced in the course of implementation, as well as the new theoretical insights into quantum dynamics the work has led to. We also developed QGLab – an open-source end-to-end software solution that facilitates conducting the wormhole-inspired teleportation experiments on state-of-the-art and emergent generations of QPUs supported by the Qiskit and tket SDKs. We consider our study and deliverables as an early practical step towards the realization of more complex experiments for the indirect probing of quantum gravity in the lab.