微观态可分辨性、量子复杂性和本征态热化假说
Microstate Distinguishability, Quantum Complexity, and the Eigenstate Thermalization Hypothesis
摘要：
在这项工作中，我们使用量子复杂性理论来量化区分本征态的困难服从本征态热化假设（ETH）。在用低能观测量的代数识别简单算子并追踪出互补的高能希尔伯特空间之后，ETH导致粗粒度本征态之间的迹距离的指数抑制。相反，我们表明，指数硬度的状态之间的区分意味着ETH-样的矩阵元素。Grover搜索的查询复杂度上的BBBV下界然后直接转换为复杂度理论声明下界，区分这些简化状态的难度。
英文摘要：
In this work, we use quantum complexity theory to quantify the difficulty of distinguishing eigenstates obeying the Eigenstate Thermalization Hypothesis (ETH). After identifying simple operators with an algebra of low-energy observables and tracing out the complementary high-energy Hilbert space, the ETH leads to an exponential suppression of trace distance between the coarse-grained eigenstates. Conversely, we show that an exponential hardness of distinguishing between states implies ETH-like matrix elements. The BBBV lower bound on the query complexity of Grover search then translates directly into a complexity-theoretic statement lower bounding the hardness of distinguishing these reduced states.
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