Title: Estimating time in quantum chaotic systems and black holes Show Chinese title

Title: 量子混沌系统和黑洞中的时间估计

Abstract: We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation." Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time values. Intuitively, it should become increasingly difficult to estimate the precise value of time by making measurements on the state. We use a quantity called the Fisher information from quantum metrology to quantify the minimum uncertainty in estimating time. Due to unitarity, the uncertainty in the time estimate does not grow with time if we have access to optimal measurements on the full system. Restricting the measurements to act on a small subsystem or to have low computational complexity leads to results expected from equilibration, where the time uncertainty becomes large at late times. With optimal measurements on a subsystem larger than half of the system, we regain the ability to estimate the time very precisely, even at late times. Hawking's calculation for the reduced density matrix of the black hole radiation in semiclassical gravity contradicts our general predictions for unitary quantum chaotic systems. Hawking's state always has a large uncertainty for attempts to estimate the time using the radiation, whereas our general results imply that the uncertainty should become small after the Page time. This gives a new version of the black hole information loss paradox in terms of the time estimation task. By restricting to simple measurements on the radiation, the time uncertainty becomes large. This indicates from a new perspective that the observations of computationally bounded agents are consistent with the semiclassical effective description of gravity. Show Chinese abstract

Abstract: 我们通过考虑一个假设任务“时间估计”，来描述混沌量子多体系统的动力学的新普遍特性。 混沌系统中的大多数宏观可观测量会趋于接近常数的晚期值。 直觉上，通过对状态进行测量来估计精确的时间值应该会变得越来越困难。 我们使用量子计量学中称为费舍尔信息的量来量化估计时间的最小不确定性。 由于单位性，如果我们能够对整个系统进行最优测量，时间估计的不确定性不会随时间增长。 将测量限制在小子系统上或计算复杂度较低的情况下，会得到从平衡中预期的结果，即在晚期时间不确定性变得很大。 在大于系统一半的子系统上进行最优测量，我们可以重新获得在晚期时间精确估计时间的能力。 霍金在半经典引力中对黑洞辐射的约化密度矩阵的计算与我们对单位性量子混沌系统的普遍预测相矛盾。 霍金的状态在使用辐射尝试估计时间时总是具有较大的不确定性，而我们的普遍结果表明，在页面时间之后不确定性应该变得很小。 这提供了一个新的版本的黑洞信息丢失悖论，以时间估计任务的形式表达。 通过限制对辐射进行简单的测量，时间不确定性变得很大。 这从一个新的角度表明，计算能力受限的观察者的观测结果与引力的半经典有效描述是一致的。