发表机构
Politecnico di Torino; Newcastle University（都灵理工大学; 纽卡斯尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
将广义概率理论的拟概率表示结构定理与玻色子量子纠错码联系起来，为连续变量纠错码建立一般相空间表示，并具体给出GKP码、猫码和二项式码的相空间表示，定义误差在相空间中的数学结构。
AI 中文摘要
在本文中，我们将广义概率理论的拟概率表示结构定理与玻色子量子纠错码联系起来，为连续变量纠错码提供了一般相空间表示，并具体展示了通过该方法获得的Gottesman-Knill-Preskill码、猫码和二项式码的相空间表示。这种表示使我们能够从一般角度以及针对每种码定义误差在相空间中可能采取的数学结构，我们既抽象地展示了这一点，也针对单光子丢失误差的具体例子进行了说明。
英文摘要
We connect the structure theorem for quasiprobability representations to quantum error correction. For a code space invariant under a subgroup of an extended Weyl-Heisenberg group, the Brif-Mann construction gives a semi-functorial representation whenever its kernel satisfies the Stratonovich-Weyl axioms, and composes on channels covering full error-correction cycles. With phase-space parity available, a kernel other than the ordinary Wigner one exists iff the code space is invariant under a lattice of displacements: among compact-phase-space bosonic codes, this is only the ideal Gottesman-Kitaev-Preskill family; in finite dimension, this is every qudit stabiliser code, whose negative volume for odd prime dimension is the syndrome-averaged logical magic. For rotation-symmetric, one-photon, non-Pauli qudit and spin codes only the ordinary kernel remains, its negativity reflecting the physical carrier, not logical content; a sector-graded representation built from recovery isometries restores a resource reading. We add a channel atlas, a closed-form magic lifetime under displacement noise, a Kirkwood-Dirac layer, and finite-energy corrections.
Comments32+12 pages, no figures. Accepted for publication in Phys Rev Research - matches accepted version
