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.
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BibTeX
@misc{joshi2026clifford,
title = {{Clifford and Haar scramblers yield equal mean fidelity but unequal fluctuations in black hole-inspired teleportation}},
author = {Sudhanva Joshi and Sunil Kumar Mishra},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.19180},
eprint = {2606.19180},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.19180},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Clifford and Haar scramblers yield equal mean fidelity but unequal fluctuations in black hole-inspired teleportation
AU - Sudhanva Joshi
AU - Sunil Kumar Mishra
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2606.19180
UR - https://arxiv.org/abs/2606.19180
AB - 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.
ER -