Local Unitary Invariants of Generic Multi-qubit States

Naihuan Jing, Shao-Ming Fei, Ming Li, Xianqing Li-Jost, and Ting-Gui Zhang

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Submission date: 12. Aug. 2015
Pages: 7
published in: Physical review / A, 92 (2015) 2, art-no. 022306 
DOI number (of the published article): 10.1103/PhysRevA.92.022306
Bibtex
with the following different title: Local unitary invariants of generic multiqubit states
PACS-Numbers: 03.67.-a, 02.20.Hj, 03.65.-w
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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.