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Path-entangled two qubit states have been generated in laboratory settings on silicon photonic chips in recent years, making important steps in the direction of generating optical cluster states. Among methods of doing this, it has been shown experimentally that spontaneous [[four-wave mixing]] can be used with the appropriate use of [[optical ring resonators|microring resonators]] and other [[waveguide]]s for filtering to perform on-chip generation of two-photon Bell states, which are equivalent to two-qubit cluster states up to local unitary operations.
[[File:FWM_energy_levels.png|thumb]]
To do this, a short [[laser]] pulse is injected into an on-chip waveguide that splits into two paths. This forces the pulse into a superposition of the possible directions it could go. The two paths are coupled to microring resonators that allow circulation of the laser pulse until spontaneous four-wave mixing occurs, taking two photons from the laser pulse and converting them into a pair of photons, called the signal <math>s</math> and idler <math>i</math> with different frequencies in a way that conserves energy. In order to prevent the generation of multiple photon pairs at once, the procedure takes advantage of the conservation of energy and ensures that there is only enough energy in the laser pulse to create a single pair of photons. Because of this restriction, spontaneous four-wave mixing can only occur in one of the microring resonators at a time, meaning that the superposition of paths that the laser pulse could take is converted into a superposition of paths the two photons could be on. Mathematically, if <math>|\alpha\rangle</math> denotes the laser pulse, the paths are labeled as <math>a</math> and <math>b</math>, the process can be written as
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