Local unitary equivalence of generic multi-qubits based on the CP decomposition
arXiv:2205.06422 · doi:10.1007/s10773-022-05106-w
Abstract
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 -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.
arXiv comment23 pages, 2 figures
References in corpus (16)
- Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations
- Non-local properties of multi-particle density matrices
- Local unitary equivalence of multipartite pure states
- Local unitary equivalence and entanglement of multipartite pure states
- Local Unitary Classification of Arbitrary Dimensional Multipartite Pure States
- Nonlocal Properties and Local Invariants for Bipartite Systems
- Local Invariants for a Class of Mixed States
- Local Unitary Equivalence of Arbitrary Dimensional Bipartite Mixed Quantum States
- Local Unitary Equivalence of Multi-qubit Mixed quantum States
- Criterion of Local Unitary Equivalence for Multipartite States
- Local Unitary Invariants of Generic Multi-qubit States
- Classification of Arbitrary Multipartite Entangled States under Local Unitary Equivalence
- SLOCC Invariants for Multipartite Mixed States
- A Note on Equivalence of Bipartite States under Local Unitary Transformations
- Necessary and Sufficient Conditions for Local Unitary Equivalence of Multi-qubit States
- Local unitary equivalence of quantum states and simultaneous orthogonal equivalence