Clifford and Haar scramblers yield equal mean fidelity but unequal fluctuations in black hole-inspired teleportation

Abstract:Quantum information transfer between entangled black holes has inspired many-body teleportation protocols. We study such a protocol without assuming a gravitational dual and ask whether its fidelity requires nonstabilizerness, or magic, in the scrambling dynamics. Because the mean fidelity depends only on the third moments of the scrambler ensemble, zero-magic Clifford scramblers teleport on average as well as Haar-random unitaries. Solving the protocol exactly at infinite temperature, we find that typical Clifford scramblers approach perfect teleportation while the magic of the complete circuit vanishes as the inverse system size. The two ensembles nevertheless differ in their fluctuations: the exact Clifford fidelity variance decays only algebraically with system size, whereas the Haar variance is exponentially small. This separation characterizes the ensembles rather than magic itself, since magic added away from the message qubit can leave every fidelity statistic unchanged. With a decoder uncorrelated with the scrambler, every unitary 2-design leaves the mean fidelity at the no-transfer value, whatever its magic.

8 pages. To be communicated to a Journal soon. Comments will be highly appreciated

arXiv:2606.19180 [quant-ph]

(or arXiv:2606.19180v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.19180 Focus to learn more arXiv-issued DOI via DataCite

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