Efficient decoding for the Hayden-Preskill protocol

By B. Yoshida, Alexei Y. Kitaev. 2017

180 citations recorded by the source corpus.

We present two particular decoding procedures for reconstructing a quantum state from the Hawking radiation in the Hayden-Preskill thought experiment. We work in an idealized setting and represent the black hole and its entangled partner by $n$ EPR pairs. The first procedure teleports the state thrown into the black hole to an outside observer by post-selecting on the condition that a sufficient number of EPR pairs remain undisturbed. The probability of this favorable event scales as $1/d_{A}^2$, where $d_A$ is the Hilbert space dimension for the input state. The second procedure is deterministic and combines the previous idea with Grover's search. The decoding complexity is $\mathcal{O}(d_{A}\mathcal{C})$ where $\mathcal{C}$ is the size of the quantum circuit implementing the unitary evolution operator $U$ of the black hole. As with the original (non-constructive) decoding scheme, our algorithms utilize scrambling, where the decay of out-of-time-order correlators (OTOCs) guarantees faithful state recovery.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/13fdee0b03ad3d2e90a068a3fdcfb008b1c6a060

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Citations in the corpus

Information flow in black hole evaporation (2019, background): “This analogy might be made more precise by regarding the shock wave as a ‘heavy diary’, as discussed in [1] – see also [59].”
The quantum gravity dynamics of near extremal black holes (2018, background): “It might also be interesting to consider the black hole information paradox [42] and late time traversable wormholes including the quantum fluctuations of the boundary [36, 37, 38, 39, 45].”
Scrambling Dynamics and Out-of-Time-Ordered Correlators in Quantum Many-Body Systems (2022, methodology): “A representative model in this class is the Sachdev-Ye-Kitaev model [142, 143] (also see a recent review [144]) describing a cluster of N interacting Majorana fermions, H = ∑ i1 i2 i3 i4 ji1i2i3i4χi1χi2χi3χi4, (C18) where χi is Majorana operator obeying the usual commutator {χi, χj} = δij .”