在哈恩自旋回波的意义上进行概括，我们完全描述了有效多量子位相互作用的那些么正传播子的特征，这些么正传播子可以仅通过\em量子位上的{ \em本地}么正操作来反转（自旋- $\tfrac{1}{2}$）。$U\in \mathbf{SU}(2^n)$的子集满足$U^{-1}=K_1 U K_2$和局部酉对$K_1, K_2\in\mathbf{SU}(2)^{\otimes n}$，包括两个类：在类型I中，$K_1$和$K_2$彼此逆，而在类型II中，它们不是。{类型-I}由可以针对所有时间$t\in\R{}$联合反转的单参数组组成，因为它们的哈密顿生成元满足$K H K^{-1} = \Ad K (H) = -H$。由于所有生成局部可逆幺正的I型Hamilton算子都被与{ \em local}共轭映射$\Ad K$的本征值-1相关的本征空间所张成，因此本征空间可以用封闭的代数形式给出。指出了与$\mathfrak{sl}(N,\C{})$的根空间分解的关系。特殊情况下，I型可逆哈密顿是$p$ -量子顺序，并分析了球形张量的$p$顺序的变换性质。有效的多量子位相互作用哈密顿量的特征在于通过其耦合拓扑图。{Type-II}由逐点局部可逆传播子组成，其中一部分可以根据其矩阵表示的对称性进行分类。此外，我们显示梯度流数值求解的决定问题，无论是传播是I型或II型可逆或不驱动的最小二乘距离$\norm{K_1 e^{-itH} K_2 - e^{+itH}}^2_2$为零。
英文摘要：
Generalising in the sense of Hahn's spin echo, we completely characterise those unitary propagators of effective multi-qubit interactions that can be inverted solely by {\em local} unitary operations on $n$ qubits (spins-$\tfrac{1}{2}$). The subset of $U\in \mathbf{SU}(2^n)$ satisfying $U^{-1}=K_1 U K_2$ with pairs of local unitaries $K_1, K_2\in\mathbf{SU}(2)^{\otimes n}$ comprises two classes: in type-I, $K_1$ and $K_2$ are inverse to one another, while in type-II they are not. {Type-I} consists of one-parameter groups that can jointly be inverted for all times $t\in\R{}$ because their Hamiltonian generators satisfy $K H K^{-1} = \Ad K (H) = -H$. As all the Hamiltonians generating locally invertible unitaries of type-I are spanned by the eigenspace associated to the eigenvalue -1 of the {\em local} conjugation map $\Ad K$, this eigenspace can be given in closed algebraic form. The relation to the root space decomposition of $\mathfrak{sl}(N,\C{})$ is pointed out. Special cases of type-I invertible Hamiltonians are of $p$-quantum order and are analysed by the transformation properties of spherical tensors of order $p$. Effective multi-qubit interaction Hamiltonians are characterised via the graphs of their coupling topology.
{Type-II} consists of pointwise locally invertible propagators, part of which can be classified according to the symmetries of their matrix representations. Moreover, we show gradient flows for numerically solving the decision problem whether a propagator is type-I or type-II invertible or not by driving the least-squares distance $\norm{K_1 e^{-itH} K_2 - e^{+itH}}^2_2$ to zero.
Hierarchies among genuine multipartite entangling capabilities of quantum gates
Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute（哈里什-钱德拉研究所，霍米·巴巴国立学院下属机构）；Gandhi Institute of Technology and Management (Deemed to be University)（甘地科技与管理学院（视为大学））
Informationally Complete Distributed Metrology Without a Shared Reference Frame
University of Science and Technology of China（中国科学技术大学）；Anhui Province Key Laboratory of Quantum Network（安徽省量子网络重点实验室）；CAS Center For Excellence in Quantum Information and Quantum Physics（中国科学院量子信息与量子物理学前沿卓越创新中心）；Hefei National Laboratory（合肥国家实验室）
Quantum Spectral Authentication: Entity Authentication and Key Derivation from a Hidden Eigenstate of a Public Unitary Challenge
University of Technology Sydney（悉尼科技大学）；Centre for Quantum Software and Information, University of Technology Sydney（悉尼科技大学量子软件与信息中心）；Data61, CSIRO（CSIRO数据六一分部）；Institute of Computer Science, Polish Academy of Sciences（波兰科学院计算机科学研究所）
Matrix-product operator dualities in integrable lattice models
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo（东京大学宇宙物理数学研究所（WPI））；University of Vienna, Faculty of Mathematics（维也纳大学数学系）；St John’s College and Mathematical Institute, University of Oxford（牛津大学圣约翰学院和数学研究所）
