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We describe an efficient way of measuring the concurrence for the hyperentanglement. In this protocol, the hyperentangled state is encoded in both the polarization and the momentum degrees of freedom. We show that measurement of the concurrences of both polarization and momentum entanglements can be conversed into the measurement of the total probability of picking up the odd-parity state and can be measured directly. This protocol requires the weak cross-Kerr nonlinearity to construct the quantum nondemolition measurement and does not require the sophisticated controlled-not gate operation. It is feasible in future experimental technology.

Two-step measurement of the concurrence for hyperentangled state