无恢复操作的粒子损失下CHSH非局域性的恢复
Recovery-Free CHSH Nonlocality with Particle Loss
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中文总结 AI 辅助
该研究探究粒子损失下无恢复操作时CHSH非局域性的存活情况，构建多类无恢复协议，明确不同存活概率下的CHSH违背条件，区分损耗与测量带来的不同限制。
中文摘要 AI 辅助
CHSH非局域性能否在不应用显式恢复操作的情况下在粒子损失中存活？原则上，任何确定性恢复都可被吸收到测量中。从操作层面，我们证明答案取决于对损耗系统允许的测量。我们区分两种情况：标记擦除（每个损失的粒子留下可检测记录）与未标记删除（无此类记录残留）。对于标记擦除且存活概率η>1/2，利用已知量子容量结果，我们证明测量可渐近逼近量子最大值2√2；相反，η≤1/2时，两种损耗模型下均无法实现CHSH违背。随后，我们构造基于n量子比特Dicke态|D_N^n⟩的置换不变编码的显式无恢复协议，仅对存活粒子进行测量：单激发（N=1）编码在η>1/√2时违背CHSH，增加激发数N可得到一系列协议，在η>η_G=(√5-1)/2时违背CHSH，N→∞时渐近逼近黄金比例η_G。最后，我们提出稀疏删除二项式置换不变协议，保证在O(√n)个删除误差内实现CHSH违背。我们的结果区分了损耗施加的基本限制与无恢复的显式测量设定的限制。
英文摘要
Can CHSH nonlocality survive particle loss without applying an explicit recovery operation? In principle, any deterministic recovery can be absorbed into the measurement. Operationally, we show that the answer depends on the allowed measurements on the lossy system. We distinguish flagged erasure, in which each lost particle leaves a detectable record, from unflagged deletion, in which no such record remains. For flagged erasure and survival probability $η>1/2$, using known quantum-capacity results, we show measurements that asymptotically approach the quantum maximum $2\sqrt2$. In contrast, for $η\le1/2$, CHSH violation is impossible for both loss models. Then, we construct explicit recovery-free protocols using permutation-invariant encodings built from $n$-qubit Dicke states $| D_N^n\rangle$ and measurements on the surviving particles. A one-excitation $(N=1)$ encoding violates CHSH for $η>1/\sqrt{2}$. Increasing the excitation number $N$ yields a family of protocols that violates CHSH for $η>η_G=(\sqrt{5}-1)/2$, with the asymptotic golden ratio approached as $N \to \infty$. Finally, we present a sparse-deletion binomial PI protocol that guarantees CHSH violation for up to $O(\sqrt n)$ deletion errors. Our results distinguish fundamental limits imposed by loss from those set by explicit measurements without recovery.
