闭环：非因果计算、部分轨迹与后选择纠缠
Tracing the Loop: Non-Causal Computation, Partial Traces, & Postselected Entanglement
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中文总结 AI 辅助
本文通过范畴论将非因果电路与后选择量子隐形传态关联，证明经典逻辑一致性等价于贝尔后选择概率为1/d^2，并识别保持线性依赖的量子构造。
中文摘要 AI 辅助
本文对Baumeler和Wolf的逻辑一致非因果电路给出了范畴论解释，并将其与后选择量子隐形传态联系起来。环回反馈由非负矩阵范畴中的迹表示，并证明了当且仅当诱导的环转移矩阵对每个外部输入具有迹$1$时，被求迹的过程是随机的，该条件被证明等价于对确定性电路的每个输入，环具有唯一不动点。经典非因果电路由带内部寄存器的测量-制备量子信道表示，该寄存器利用最大纠缠的贝尔态并进行后选择。主要结果是，经典逻辑一致性等价于后选择贝尔结果对每个经典输入分布具有精确概率$1/d^2$（其中$d$为环维度）。随后归一化的条件输出与经典范畴迹完全一致。这项工作识别了一类量子贝尔后选择构造，其条件演化保持对经典输入分布的线性依赖。
英文摘要
This paper gives a categorical interpretation of Baumeler \& Wolf's logically consistent non-causal circuits, connecting them to postselected quantum teleportation. Looped feedback is represented by a trace in the category of non-negative matrices, and it is shown that the traced process is stochastic precisely when the induced loop transition matrix has trace $1$ for every external input, a condition shown to be equivalent to a unique fixed point for the loop for each input to a deterministic circuit. A classical non-causal circuit is represented by a measure-and-prepare quantum channel with an internal register utilising a maximally entangled Bell-state with postselection. The main result is that classical logical consistency is equivalent to the postselected Bell outcome having, for loop dimension $d$, probability exactly $1/d^2$ for each classical input distribution. The subsequent normalised conditional output then agrees exactly with the classical categorical trace. This work identifies a class of quantum Bell-postselection constructions whose conditional evolution maintains linear dependence on classical input distributions.
发表机构
- Quantum Village Inc.（量子村有限公司）
机构由 AI 辅助整理，请以论文原文为准。
