AI 中文总结
研究将时间反转对称性应用于量子码，推导其对物理错误代数的奇偶选择规则，发现偶权Knill–Laflamme条件自动成立，还重新解释了Rains影子枚举器，为量子纠错提供新的理论视角。
AI 中文摘要
我们将时间反转对称性应用于量子码，证明其会对物理错误代数施加奇偶选择规则。奇数个自旋上的时间反转不变逻辑量子比特是一个Kramers二重态，迫使所有偶权Pauli算子表现为标量。因此，所有偶权Knill–Laflamme条件自动成立，单量子比特错误检测即意味着可纠正。我们随后通过时间反转重新解释Rains影子枚举器：每个系数是码与其时间反转像之间经错误解析的重叠之和。
英文摘要
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.
