Quantum information with even and odd states of orbital angular momentum of light

•We propose to use even and odd states of orbital angular momentum (OAM) of light for quantum information tasks.•We describe the OAM qubits and entangled states in even/odd basis and the corresponding projective operators.•We present a method for the tomography and the Bell's inequality violation for photons entangled in even/odd OAM states.•We also describe hyper and hybrid entanglement of even/odd OAM states along with polarization and their applications.

We address the possibility of using even/odd states of orbital angular momentum (OAM) of photons for the quantum information tasks. Single photon qubit states and two photon entangled states in even/odd basis of OAM are considered. We present a method for the tomography and general projective measurement in even/odd basis. With the general projective measurement, we show the Bell violation and quantum cryptography with Bell's inequality. We also describe hyper and hybrid entanglement of even/odd OAM states along with polarization, which can be applied in the implementation of quantum protocols like super dense coding.