标题： 协议诱导的Dicke态上的动态代数 显示英文标题

标题： A dynamical algebra of protocol-induced transformations on Dicke states

摘要： 量子$n$-比特态在量子信息的重要算法和应用中是基本要素。 因此，人们对开发制备和操作Dicke态的方法表现出浓厚的兴趣，这些态构成了完全对称态子空间的基底。 考虑了两种转换Dicke态的简单协议。 通过Weyl代数$W(2)$和$\mathfrak{su}(2)$对这些协议所引起的操作进行了代数表征。 明确确定了同时应用两种协议后的固定点。 强调了与二进制Hamming方案、Hadamard变换和Krawtchouk多项式之间的联系。 显示英文摘要

摘要： Quantum $n$-qubit states that are totally symmetric under the permutation of qubits are essential ingredients of important algorithms and applications in quantum information. Consequently, there is significant interest in developing methods to prepare and manipulate Dicke states, which form a basis for the subspace of fully symmetric states. Two simple protocols for transforming Dicke states are considered. An algebraic characterization of the operations that these protocols induce is obtained in terms of the Weyl algebra $W(2)$ and $\mathfrak{su}(2)$. Fixed points under the application of the combination of both protocols are explicitly determined. Connections with the binary Hamming scheme, the Hadamard transform, and Krawtchouk polynomials are highlighted.