Direct measurement of the concurrence for two-photon polarization entangled pure states by parity-check measurements

• Direct measurement of two-photon polarization entanglement is proposed.
• The concurrence can be obtained without prior quantum state tomography.
• The entangled photons donʼt annihilate during the concurrence measuring process.
• The protocol is feasible with the help of the weak cross-Kerr nonlinearity.
• The direct measurement scheme works for both local and remote entanglement.

We present a protocol for directly measuring the concurrence of a two-photon polarization entangled pure or mixed state without prior quantum state tomography. By parity-check measurements and simple operations on two copies of the two-photon polarization entangled pure state, the concurrence is encoded in the total probability of picking up the odd parity states from the signal states. This protocol makes use of highly efficient homodyne detection, and it could be feasible in the near future with the help of the weak cross-Kerr nonlinearity. Moreover, our protocol can be used in a distributed fashion to directly determine the entanglement of remote states, which may find its important applications in quantum communication.