Unscrambling Quantum Information with Clifford decoders (2212.11337v5)

Abstract: Quantum information scrambling is a unitary process that destroys local correlations and spreads information throughout the system, effectively hiding it in nonlocal degrees of freedom. In principle, unscrambling this information is possible with perfect knowledge of the unitary dynamics [B. Yoshida and A. Kitaev, arXiv:1710.03363.]. However, this Letter demonstrates that even without previous knowledge of the internal dynamics, information can be efficiently decoded from an unknown scrambler by monitoring the outgoing information of a local subsystem. Surprisingly, we show that scramblers with unknown internal dynamics, which are rapidly mixing but not fully chaotic, can be decoded using Clifford decoders. The essential properties of a scrambling unitary can be efficiently recovered, even if the process is exponentially complex. Specifically, we establish that a unitary operator composed of $t$ non-Clifford gates admits a Clifford decoder up to $t\le n$.