对称多重量子态：恒星，纠缠，旋转传感器
Symmetric Multiqudit States: Stars, Entanglement, Rotosensors
摘要：
一个由$N=d-1$组成的马约拉纳星星座表示一个任意的纯量子态，其维数为$d$，或者是一个由$n$量子比特组成的系统的置换对称态。我们推广后者的建设，以类似的方式表示任意对称纯态的$k$子系统与$d$水平。对于$d\geq 3$，就旋转而言，这些状态等价于具有确定的相对复权重的各种自旋状态的集合。马约拉纳的领导下，我们引入了一个多星座，由上述自旋状态的马约拉纳星座，增强了辅助，“观众”星座，编码的复杂的权重。四qutrits的对称态的恒星表示的例子，和两个自旋$3/2$系统，提出。我们重新审视厄米和Murnaghan同构，其中涉及各种自旋，党的数量，甚至对称性的多体状态。我们展示了如何引入的工具可以用来分析多体纠缠，并确定最佳的量子旋转传感器，即，纯态对围绕指定轴的旋转最敏感，或者在所有轴上平均。
英文摘要：
A constellation of $N=d-1$ Majorana stars represents an arbitrary pure quantum state of dimension $d$ or a permutation-symmetric state of a system consisting of $n$ qubits. We generalize the latter construction to represent in a similar way an arbitrary symmetric pure state of $k$ subsystems with $d$ levels each. For $d\geq 3$, such states are equivalent, as far as rotations are concerned, to a collection of various spin states, with definite relative complex weights. Following Majorana's lead, we introduce a multiconstellation, consisting of the Majorana constellations of the above spin states, augmented by an auxiliary, "spectator" constellation, encoding the complex weights. Examples of stellar representations of symmetric states of four qutrits, and two spin-$3/2$ systems, are presented. We revisit the Hermite and Murnaghan isomorphisms, which relate multipartite states of various spins, number of parties, and even symmetries. We show how the tools introduced can be used to analyze multipartite entanglement and to identify optimal quantum rotosensors, i.e., pure states which are maximally sensitive to rotations around a specified axis, or averaged over all axes.
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