论文标题
微晶酸盐的区分性，量子复杂性和本征态热假设
Microstate Distinguishability, Quantum Complexity, and the Eigenstate Thermalization Hypothesis
论文作者
论文摘要
在这项工作中，我们使用量子复杂性理论来量化遵守本征态热假说（ETH）的特征态的难度。在识别出具有低能可观察力的代数并追踪互补的高能量希尔伯特空间的简单操作员之后，ETH会导致对粗粒菌属之间的痕量距离的指数抑制。相反，我们表明，区分状态的指数硬度意味着类似伦理的矩阵元素。在Grover搜索的查询复杂性上，BBBV的下限直接转化为复杂性理论陈述，从而降低了区分这些降低状态的硬度。
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.
