We propose a passive all optical device capable of transforming the orbital angular momentum (OAM) state of light conditioned over the polarization states. The efficiency of this device is ensured due to its linear optical nature. As applications of this device, we show CNOT and SWAP operations between polarization and OAM qubits, non-interferometric OAM mode sorter and generalized Pauli X operation on a four-dimensional subspace of OAM.
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