论文标题
高温热化意味着量子状态设计的出现
High-temperature thermalization implies the emergence of quantum state designs
论文作者
论文摘要
最近观察到，在某些热化多体系统中，测量了一个子系统的补充，该子系统以适当的正顺序为无限温度的子系统的补充会导致近似量子状态k-designs作为子系统上的测量后态。我们证明，近似K-Designs的这种出现在每个大型系统接近最大混合的大型系统中都是正确的。在技术层面上，我们表明，当以合适的正顺序基础测量时，大约最大混合状态的任何高维纯化都会引起近似量子状态k-design。此外，我们表明，对于从HAAR测量中随机选择的测量底座的压倒性概率是正确的。
It was recently observed that in certain thermalizing many-body systems, measuring the complement of a subsystem that thermalized to infinite temperature in a suitable orthonormal basis gives rise to approximate quantum state k-designs as post-measurement states on the subsystem. We prove that this emergence of approximate k-designs holds true in every large system where some small subsystem is close to being maximally mixed. On a technical level we show that any high-dimensional purification of an approximately maximally mixed state induces an approximate quantum state k-design when measured in a suitable orthonormal basis. Moreover, we show that this is true with overwhelming probability for measurement bases chosen uniformly at random from the Haar measure.
