The distiction between classical product states and quantum entangled states is disclosed with examples. Spontaneous parametric down conversion as a source of entangled photons is described. The action of a perfect beam splitter is analysed using creation and annihilation operators. The HOM interferometer is described. Its use in demonstrating the indistinguishability of photons and in measuring bandwidth of sources at the level of femtoseconds is recounted. Two particle entanglement is analysed using the Bloch sphere representation showing how the full knowledge of the entangled state does not fix the state of the individual particles. The four Bell states, eigenstates of two particle entanglement, are introduced. Teleportation of a photon state using entangled photons is described, and an experiment to entangle the quantum states of atoms at space-like separation outlined.
Implementing a multi-target-qubit controlled-not gate with logical qubits outside a decoherence-free subspace and its application in creating quantum entangled states
