满秩噪声禁止长距离纠缠交换
Full-Rank Noise Forbids Long-Range Entanglement Swapping
- Stony Brook University（石溪大学）
- Rensselaer Polytechnic Institute（伦斯勒理工学院）
- Harvard University（哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明满秩噪声禁止量子中继器长距离纠缠交换，提出谱参数判据，并构造秩亏链路态族以维持纠缠，实验验证了秩的影响。
AI中文摘要：
量子中继器通过交换噪声基本链路来扩展纠缠。我们证明满秩噪声在长距离上禁止这种操作：对于任何纠缠的满秩两量子比特链路，存在一个有限深度，超过该深度，无论中间量子比特上的测量结果如何，甚至在任何自适应后选择策略下，都无法建立端到端的纠缠。这一限制由链路的一个谱参数决定，为中继器路由提供了不可行性判据。相比之下，我们构造了秩为三和秩为二的链路态族，它们允许后选择测量结果分支具有指数小的概率，但在每个有限深度上具有严格正的并发度。在超导处理器上的交换实验表明，具有相同初始并发度但不同秩的链路在后选择交换下表现不同。在多体物理的语言中，该链是一个矩阵乘积密度算子，满秩键禁止长距离可局域化纠缠，而秩亏键可以维持它。
英文摘要：
Quantum repeaters extend entanglement by swapping noisy elementary links. We prove that full-rank noise forbids this at long range: for any entangled full-rank two-qubit link, there is a finite depth beyond which no end-to-end entanglement can be established regardless of the measurement outcomes on intermediate qubits, even under any adaptive postselected strategy. This limit is set by one spectral parameter of the link, giving a no-go criterion for repeater routing. In contrast, we construct link state families of rank three and rank two that admit postselected measurement outcome branches of exponentially small probability but with strictly positive concurrence at every finite depth. Swapping experiments on a superconducting processor show that links of equal initial concurrence but different rank behave differently under postselected swapping. In the language of many-body physics, the chain is a matrix-product density operator, and full-rank bonds forbid long-range localizable entanglement, while rank-deficient bonds can sustain it.
