Time-Reversal Selection Rules for Quantum Error Correction

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.

Source: arXiv:2608.06304v1 - http://arxiv.org/abs/2608.06304v1 PDF: https://arxiv.org/pdf/2608.06304v1 Original Link: http://arxiv.org/abs/2608.06304v1