Local Unitary Invariants of Generic Multi-qubit States

Abstract

We present a complete set of local unitary invariants for generic multi-qubit systems which gives necessary and sufficient conditions for two states being local unitary equivalent. These invariants are canonical polynomial functions in terms of the generalized Bloch representation of the quantum states. In particular, we prove that there are at most 12 polynomial local unitary invariants for two-qubit states and at most 90 polynomials for three-qubit states. Comparison with Makhlin's 18 local unitary invariants is given for two-quibit systems.

5 pages

References in corpus (7)

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Cited by in corpus (12)

• Direct method for measuring and witnessing quantum entanglement of arbitrary two-qubit states through Hong-Ou-Mandel interference
• On Local Unitary Equivalence of Two and Three-qubit States
• Local unitary equivalence of quantum states and simultaneous orthogonal equivalence
• Two methods for measuring Bell nonlocality via local unitary invariants of two-qubit systems in Hong-Ou-Mandel interferometers
• Local unitary equivalence of generic multi-qubits based on the CP decomposition
• Maximally entangled Rydberg-atom pairs via Landau-Zener sweeps
• Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States
• Criteria of genuine multipartite entanglement based on correlation tensors
• Volume of the set of locally diagonalizable bipartite states
• Local unitary equivalence of arbitrary-dimensional multipartite quantum states
• Bargmann-invariant framework for local unitary equivalence and entanglement
• Identifying local unitary equivalence based on reduction of quantum states