Time-Reversal Selection Rules for Quantum Error Correction

Abstract:We apply time-reversal symmetry to quantum codes and show that it imposes parity selection rules on the physical error algebra. A time-reversal-invariant logical qubit on an odd number of spins is a Kramers doublet, forcing every even-weight Pauli to act as a scalar. Consequently, all even-weight Knill--Laflamme conditions hold automatically, so single-qubit error detection implies correction. We then reinterpret the Rains shadow enumerator through time reversal: each coefficient is a sum of error-resolved overlaps between a code and its time-reversed image.

arXiv:2608.06304 [quant-ph]

(or arXiv:2608.06304v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.06304 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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