标题： 随机监控量子码 显示英文标题

标题： Randomly Monitored Quantum Codes

摘要： 量子测量传统上被视为量子信息处理的最后一步，这对于读取处理后的信息是必不可少的，但会将量子态坍缩为经典态。 然而，最近的研究表明，量子测量本身可以引发新的量子现象。 一个具有开创性的例子是受监控的随机电路，它能够比随机酉电路更快地生成长程纠缠。 受这些结果的启发，本文探讨了以下问题：当量子信息被编码在量子纠错码中时，需要随机测量多少个物理量子比特才能破坏编码的信息？ 我们对各种量子纠错码进行了研究，并推导出通过测量破坏信息的必要且充分条件。 特别是，我们证明对于一大类量子纠错码，当仅有一小部分物理量子比特未被测量时，通过随机单量子比特泡利测量无法破坏编码的信息。 我们的结果不仅揭示了量子码在测量退相干下的非凡鲁棒性，还暗示了在量子信息处理任务中的潜在应用。 显示英文摘要

摘要： Quantum measurement has conventionally been regarded as the final step in quantum information processing, which is essential for reading out the processed information but collapses the quantum state into a classical state. However, recent studies have shown that quantum measurement itself can induce novel quantum phenomena. One seminal example is a monitored random circuit, which can generate long-range entanglement faster than a random unitary circuit. Inspired by these results, in this paper, we address the following question: When quantum information is encoded in a quantum error-correcting code, how many physical qubits should be randomly measured to destroy the encoded information? We investigate this question for various quantum error-correcting codes and derive the necessary and sufficient conditions for destroying the information through measurements. In particular, we demonstrate that for a large class of quantum error-correcitng codes, it is impossible to destroy the encoded information through random single-qubit Pauli measurements when a tiny portion of physical qubits is still unmeasured. Our results not only reveal the extraordinary robustness of quantum codes under measurement decoherence, but also suggest potential applications in quantum information processing tasks.