Information-Theoretic Measure of Genuine Multi-Qubit Entanglement

We consider pure quantum states of N qubits and study the genuine N-qubit entanglement that is shared among all the N qubits. We introduce a information-theoretic measure of genuine N-qubit entanglement based on bipartite partitions. When N is an even number, this measure is presented in a simple formula, which depends only on the purities of the partially reduced density matrices. It can be easily computed theoretically and measured experimentally. When N is an odd number, the measure can also be obtained in principle