单次量子测量勾勒量子多体态
Single-shot quantum measurements sketch quantum many-body states
AI总结：
提出基于测量结果的非线性“测量能量”和迭代有效Hamiltonian方法，高效提取量子多体系统的最大似然状态，调和不可对易可观测量，并在长程费米子与Kitaev自旋液体模型中验证准确性。
摘要：
量子测量是我们观察由大量微观自由度组成的量子系统的眼睛。然而，量子测量的内禀不确定性和指数级大的Hilbert空间对测量结果的简单解释构成了自然障碍。我们提出一种基于测量结果的非线性“测量能量”以及迭代有效Hamiltonian方法，以高效且通用的方式提取最可能的状态（最大似然估计），从而调和不可对易可观测量并从量子测量中获取更多信息。我们在随机长程费米子模型和Kitaev量子自旋液体模型上展示了我们视角的通用性和准确性，这些模型此前缺乏确凿的特征证据。我们的研究还为非线性算符Hamiltonian等概念以及母Hamiltonian重构等应用铺平了道路。
英文摘要：
Quantum measurements are our eyes to the quantum systems consisting of a multitude of microscopic degrees of freedom. However, the intrinsic uncertainty of quantum measurements and the exponentially large Hilbert space pose natural barriers to simple interpretations of the measurement outcomes. We propose a nonlinear "measurement energy" based upon the measurement outcomes and an iterative effective-Hamiltonian approach to extract the most probable states (maximum likelihood estimates) in an efficient and general fashion, thus reconciling the non-commuting observables and getting more out of the quantum measurements. We showcase the versatility and accuracy of our perspective on random long-range fermion models and Kitaev quantum spin liquid models, where smoking-gun signatures were lacking. Our study also paves the way towards concepts such as nonlinear-operator Hamiltonian and applications such as parent Hamiltonian reconstruction.
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