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arXiv · 1507.02832

Local Unitary Invariants of Generic Multi-qubit States

Naihuan Jing·Shao-Ming Fei·Ming Li·Xianqing Li-Jost·Tinggui Zhang
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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.

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Naihuan Jing, Shao-Ming Fei, Ming Li, Xianqing Li-Jost, Tinggui Zhang. 2015-07-10. Local Unitary Invariants of Generic Multi-qubit States. https://doi.org/10.1103/physreva.92.022306

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