Necessary and Sufficient Conditions for Local Unitary Equivalence of Multi-qubit States

Abstract

We derive necessary and sufficient conditions for the LU-equivalence of two general (pure or mixed) $n$-qubit states as well as we determine the local unitary operators connecting them. Almost all relevant information is contained in the $1$-qubit reduced matrices of the multiqubit states under investigation Our technique relies on identifying {\it ab initio} all local symmetries and the corresponding local cyclic unitary operators. To derive the above conditions we use the reference forms of the multiqubit states whose definition requires the diagonalization of the 1-qubit reduced matrices. Based on those conditions we propose a straightforward protocol to decide wether or not two $n$-qubit states are LU-equivalent.

References in corpus (14)

• Quantum entanglement
• On the reality of the quantum state
• Probabilistic theories with purification
• Computing Local Invariants of Qubit Systems
• Non-local properties of multi-particle density matrices
• On local invariants of pure three-qubit states
• Local unitary equivalence of multipartite pure states
• Local unitary equivalence and entanglement of multipartite pure states
• Measurable nonlocal effect of bipartite system during a local cyclic evolution of its subsystem
• Local Invariants for a Class of Mixed States
• Local Unitary Equivalence of Arbitrary Dimensional Bipartite Mixed Quantum States
• Entanglement quantification by local unitaries
• Local Unitary Equivalence of Multi-qubit Mixed quantum States
• Criterion of Local Unitary Equivalence for Multipartite States

Cited by in corpus (8)

• Local unitary symmetries of hypergraph states
• Local Unitary Invariants of Generic Multi-qubit States
• On Local Unitary Equivalence of Two and Three-qubit States
• Local unitary equivalence of quantum states and simultaneous orthogonal equivalence
• Local unitary equivalence of generic multi-qubits based on the CP decomposition
• Local unitary equivalence of arbitrary-dimensional multipartite quantum states
• Identifying local unitary equivalence based on reduction of quantum states
• Bargmann-invariant framework for local unitary equivalence and entanglement