We introduce Transition states (T states), denoted by $\ket{T_k^n}$, as a class of multipartite entangled states characterized by a fixed number of state transitions between adjacent qubits. These states form equal-amplitude superpositions over all states with a specified transition count. Unlike Bell states based on two-qubit correlations, GHZ states characterized by global correlations among all qubits, and W and Dicke states based on fixed numbers of qubit excitations, T states are defined by transition counts along an ordered sequence of qubits. We prove that T states are unitarily equivalent to Dicke states through a chain of CX (controlled-X) operations, thereby establishing a direct correspondence between transition-based and excitation-based representations of multipartite entanglement.

翻译：我们引入跃迁态（T态），记为$\ket{T_k^n}$，作为一类由其相邻量子比特间固定数目的状态跃迁所表征的多方纠缠态。这些态在所有具有指定跃迁数的态上形成等振幅叠加。与基于两量子比特关联的贝尔态、由所有量子比特间全局关联刻画的GHZ态，以及基于固定量子比特激发数的W态和Dicke态不同，T态是通过沿有序量子比特序列的跃迁数来定义的。我们证明，通过一连串的CX（受控-X）操作，T态与Dicke态是幺正等价的，从而在多体纠缠的基于跃迁和基于激发的表示之间建立了直接对应关系。