标题： 受纯态启发的混合态无损后选择量子计量学 显示英文标题

标题： Pure State Inspired Lossless Post-selected Quantum Metrology of Mixed States

摘要： 给定一个依赖于未知参数的相同纯量子态组成的集合，最近的研究表明量子费舍尔信息可以无损地压缩到一个小得多样本的子集合中。 然而，推广到混合态会导致一个难以直接克服的技术挑战。 在这项工作中，我们通过揭示一种具有特征性的无损后选择测量背后的物理机制来避免这种技术性问题：虽然后选择后的量子态保持不变，但密度算符的参数导数被放大了一个因子，该因子等于后选择成功概率的倒数平方根。 这一观察不仅澄清了后选择量子计量的直觉和本质，还使我们能够发展出一个对于混合态无损后选择的数学紧凑理论。 我们发现，如果混合态的密度算符的参数导数（或者等效地，对称log导数）在密度矩阵的支持集上消失，则可以通过任意大的放大因子实现无损后选择。 我们用超分辨率成像和混合初始态的幺正编码的例子进行了说明。 我们的结果对于在退相干存在的情况下现实的后选择量子计量以及对量子信息理论中的几个问题的基础兴趣都是有用的。 显示英文摘要

摘要： Given an ensemble of identical pure quantum states that depend on an unknown parameter, recently it was shown that the quantum Fisher information can be losslessly compressed into a subensemble with a much smaller number of samples. However, generalization to mixed states leads to a technical challenge that is formidable to overcome directly. In this work, we avoid such technicality by unveiling the physics of a featured lossless post-selection measurement: while the post-selected quantum state is unchanged, the parametric derivative of the density operator is amplified by a large factor equal to the square root of the inverse of the post-selection success probability. This observation not only clarifies the intuition and essence of post-selected quantum metrology but also allows us to develop a mathematically compact theory for the lossless post-selection of mixed states. We find that if the parametric derivative of the density operator of a mixed state, or alternatively the symmetric logarithmic derivative, vanishes on the support of the density matrix, lossless post-selection can be achieved with an arbitrarily large amplification factor. We exemplify with the examples of superresolution imaging and unitary encoding of mixed initial states. Our results are useful for realistic post-selected quantum metrology in the presence of decoherence and of foundational interests to several problems in quantum information theory.