Rank-based SLOCC classification for odd n qubits

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We study the entanglement classification under stochastic local operations and classical communication (SLOCC) for odd n-qubit pure states. For this purpose, we introduce the rank with respect to qubit i for an odd n-qubit state. The ranks with respect to qubits 1,2,...,n give rise to the classification of the space of odd n qubits into 3ⁿ families.