Petz Recovery through a Single Polar Transformation for Approximate Quantum Error Correction

Abstract:The Petz recovery map provides a near optimal decoder for approximate quantum error correction, but its inverse square-root normalization complicates circuit implementation. We use the polar structure of the Petz recovery isometry to implement recovery through a single quantum singular value transformation (QSVT). We give explicit block-encoding circuits and an extended recovery isometry that yields approximate Petz recovery without postselection. We bound the diamond distance between the approximate and ideal Petz encoding-recovery channels in terms of a spectrum-weighted loss, which provides a channel specific objective for optimizing the QSVT angles. Uniform polynomial approximation yields an asymptotic error bound that decays exponentially with the number of QSVT iterations, at a rate controlled by the smallest nonzero scaled singular value. Applications to Haar-random encoding and the Hayden-Preskill protocol illustrate the tradeoff between circuit depth and recovery accuracy and place existing scrambling decoders within a common Petz recovery framework.

arXiv:2610.20515 [quant-ph]

(or arXiv:2610.20515v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.20515 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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