Elaboration of Linear-optical Implementations of Quantum Algorithms with Single and Double-photon Entangled States

We elaborate the use of entanglements in implementations of quantum algorithms with single and two-photon states. The dual nature of entanglement is widely exploited in many quantum problems. In Deutsch algorithm, we analyze why Hadamard gate in the single-photon implementation is not necessary for the case using EPR bi-photon states.