论文标题
基于CP分解的局部统一多数等效性
Local unitary equivalence of generic multi-qubits based on the CP decomposition
论文作者
论文摘要
candecomp/parafac（CP）分解是对矩阵对高阶张量的光谱分解的概括。在本文中，我们使用CP分解来研究高阶张量的单一等效性，并为一般高阶张量构建几个局部单一等效性的不变性。基于这种新方法，我们研究了$ 3 $ qubit状态的系数张量，并获得了CP分解的一般三方状态的局部统一等效性的必要标准。我们还概括了这种方法，以获取一些局部统一等效性的一般多目标Qudits的不变性。
The CANDECOMP/PARAFAC (CP) decomposition is a generalization of the spectral decomposition of matrices to higher-order tensors. In this paper we use the CP decomposition to study unitary equivalence of higher order tensors and construct several invariants of local unitary equivalence for general higher order tensors. Based on this new method, we study the coefficient tensors of $3$-qubit states and obtain a necessary and sufficient criterion for local unitary equivalence of general tripartite states in terms of the CP decomposition. We also generalize this method to obtain some invariants of local unitary equivalence for general multi-partite qudits.
