论文标题
通过测量
Locality and error correction in quantum dynamics with measurement
论文作者
论文摘要
光$ c $的速度对经典和量子系统的信息传递速度设定了严格的上限。在非递归量子系统中，Lieb-Robinson Theorem施加了紧急速度限制$ V \ hspace {-0.2mm} \ ll \ hspace {-0.2mm} c $，在统一进化下建立局部性并限制执行有用的量子任务所需的时间。我们将Lieb-Robinson定理扩展到用测量值扩展到量子动力学。与期望测量可以任意违反空间位置的期望相反，我们最多发现$（M \ hspace {-0.5mm} +\ hspace {-0.5mm} 1）$ - 对量子信息的速度$ v $ v $ v $ fold增强，只有$ $ $ $ $ $ $ $ $ $ $。即使经典交流是瞬时的，这也是如此，并且扩展到较弱的测量和其他非正式渠道的范围内。我们的界限在渐近上是最佳的，并且被现有的基于测量的协议饱和。我们从短期输入的初始状态中严格限制了量子计算，误差校正，传送，传送和生成纠缠的资源状态（Bell，GHz，量子，Dicke，Dicke和Spin-squeezed State）的资源要求。我们的结果对使用测量结果和主动反馈施加了限制，以加快量子信息处理，解决有关量子动力学测量本质的基本问题，并限制各种拟议的量子技术的可扩展性。
The speed of light $c$ sets a strict upper bound on the speed of information transfer in both classical and quantum systems. In nonrelativistic quantum systems, the Lieb-Robinson Theorem imposes an emergent speed limit $v \hspace{-0.2mm} \ll \hspace{-0.2mm} c$, establishing locality under unitary evolution and constraining the time needed to perform useful quantum tasks. We extend the Lieb-Robinson Theorem to quantum dynamics with measurements. In contrast to the expectation that measurements can arbitrarily violate spatial locality, we find at most an $(M \hspace{-0.5mm} +\hspace{-0.5mm} 1)$-fold enhancement to the speed $v$ of quantum information, provided the outcomes of measurements in $M$ local regions are known. This holds even when classical communication is instantaneous, and extends beyond projective measurements to weak measurements and other nonunitary channels. Our bound is asymptotically optimal, and saturated by existing measurement-based protocols. We tightly constrain the resource requirements for quantum computation, error correction, teleportation, and generating entangled resource states (Bell, GHZ, quantum-critical, Dicke, W, and spin-squeezed states) from short-range-entangled initial states. Our results impose limits on the use of measurements and active feedback to speed up quantum information processing, resolve fundamental questions about the nature of measurements in quantum dynamics, and constrain the scalability of a wide range of proposed quantum technologies.
