Multipartite states under local unitary transformations

Abstract

The equivalence problem under local unitary transformation for $n$--partite pure states is reduced to the one for $(n-1)$--partite mixed states. In particular, a tripartite system ${\mathcal{H}}_A\otimes {\mathcal{H}}_B\otimes {\mathcal{H}}_C$, where ${\mathcal{H}}_j$ is a finite dimensional complex Hilbert space for $j=A,B,C$, is considered and a set of invariants under local transformations is introduced, which is complete for the set of states whose partial trace with respect to ${\mathcal{H}}_A$ belongs to the class of generic mixed states.

Latex, 10 pages

References in corpus (8)

• Experimental quantum teleportation
• Classification of mixed three-qubit states
• A Note on Invariants and Entanglements
• Optimal Teleportation Based on Bell Measurement
• Teleportation of general finite dimensional quantum systems
• Nonlocal Properties and Local Invariants for Bipartite Systems
• Local Invariants for a Class of Mixed States
• Separability of Rank Two Quantum States

Cited by in corpus (12)

• Classification of Arbitrary Multipartite Entangled States under Local Unitary Equivalence
• A Note on Equivalence of Bipartite States under Local Unitary Transformations
• Local Equivalence of Rank-Two Quantum Mixed States
• On the algebra of local unitary invariants of pure and mixed quantum states
• Invariants for a Class of Nongeneric Three-qubit States
• Local unitary equivalent consistence for n-party states and their (n-1)-party reduced density matrices
• Representation Class and Geometrical Invariants of Quantum States under Local Unitary Transformations
• Differential Geometry of Bipartite Quantum States
• Local unitary equivalence of arbitrary-dimensional multipartite quantum states
• A Complete Set of Local Invariants for a Family of Multipartite Mixed States
• Matrix Tensor Product Approach to the Equivalence of Multipartite States under Local Unitary Transformations
• Identifying local unitary equivalence based on reduction of quantum states