Local unitary equivalence of quantum states and simultaneous orthogonal equivalence

Abstract

The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through simultaneous similarity under projective orthogonal transformations, and four parametrization independent algorithms are proposed to judge when two density matrices on ${\mathbb{C}}^{d_1}\otimes {\mathbb{C}}^{d_2}$ are locally unitary equivalent in connection with trace identities, Weierstrass pencils, Albert determinants and Smith normal forms.

13 pages

References in corpus (7)

• Quantum Teleportation Between Distant Matter Qubits
• Local Unitary Equivalence of Arbitrary Dimensional Bipartite Mixed Quantum States
• Local Unitary Equivalence of Multi-qubit Mixed quantum States
• Local Unitary Invariants of Generic Multi-qubit States
• SLOCC Invariants for Multipartite Mixed States
• Necessary and Sufficient Conditions for Local Unitary Equivalence of Multi-qubit States
• Unitary and orthogonal equivalence of sets of matrices

Cited by in corpus (6)

• Local unitary equivalence of generic multi-qubits based on the CP decomposition
• Detection of genuine tripartite entanglement based on Bloch representation of densitymatrices
• Criteria of genuine multipartite entanglement based on correlation tensors
• Detection of tripartite entanglement based on principal basis matrix representations
• Simultaneous Stoquasticity
• Local Unitary Equivalence of Tripartite Quantum States In Terms of Trace Identities