标题： 通过量子奇异值变换缓解后选择问题 显示英文标题

标题： Relieving the post-selection problem by quantum singular value transformation

摘要： 量子测量是量子信息处理中一个基础但实验上具有挑战性的组成部分。许多近期关于量子动力学的研究集中于非线性可观测量的期望值；然而，由于后选择问题——即不可控测量结果导致的巨大开销，其实验测量受到阻碍。在这项工作中，我们提出了一种基于完全量子方法的无后选择实验策略。关键思想是通过应用量子奇异值变换（QSVT）算法确定性地模拟后选择的量子态。对于纯初始态后选择，我们的方法是对固定点振幅放大的一种推广，适用于任意投影测量，实现了最优的二次加速。我们进一步通过QSVT应用线性振幅放大，将此框架扩展到混合初始态后选择，这显著提高了测量成功率。然而，由于量子编码理论施加的信息论约束，准备后选择混合态的确定性量子算法通常是不可能的。此外，我们引入了一种由测量诱导的量子隐形传态的伪逆解码器。该解码器具有一种新颖的性质，即当条件成功标志测量时，即使在信道解码器理论上不可能的情况下，解码也几乎完美。总体而言，我们的工作建立了一种强大的方法来测量新型量子动力学现象，并从量子算法的新视角理解量子动力学和量子混沌。 显示英文摘要

摘要： Quantum measurement is a fundamental yet experimentally challenging ingredient of quantum information processing. Many recent studies on quantum dynamics focus on expectation values of nonlinear observables; however, their experimental measurement is hindered by the post-selection problem -- namely, the substantial overhead caused by uncontrollable measurement outcomes. In this work, we propose a post-selection--free experimental strategy based on a fully quantum approach. The key idea is to deterministically simulate the post-selected quantum states by applying quantum singular value transformation (QSVT) algorithms. For pure initial state post-selection, our method is a generalization of fixed-point amplitude amplification to arbitrary projective measurements, achieving an optimal quadratic speedup. We further extend this framework to mixed initial state post-selection by applying linear amplitude amplification via QSVT, which significantly enhances the measurement success probability. However, a deterministic quantum algorithm for preparing the post-selected mixed state is generally impossible because of information-theoretic constraints imposed by quantum coding theory. Additionally, we introduce a pseudoinverse decoder for measurement-induced quantum teleportation. This decoder possesses the novel property that, when conditioned on a successful flag measurement, the decoding is nearly perfect even in cases where channel decoders are information-theoretically impossible. Overall, our work establishes a powerful approach for measuring novel quantum dynamical phenomena and presents quantum algorithms as a new perspective for understanding quantum dynamics and quantum chaos.