Abstract: A nonlinear crystal comprises a plurality of segments arranged along an axis, each segment being characterized by a parameter triplet comprising, a mismatch parameter, a coupling parameter, and a length of the segment, wherein an ordered multiplication of SU(1,1) matrices, each corresponding to one of the segment and being composed of hyperbolic or harmonic functions of a respective parameter triplet defines an overall SU(1,1) matrix describing sequential production of pairs of entangled photons along the axis from an incoming pump beam.

Abstract: A method for constructing a quantum gate for a unitary operation in photonic quantum information processing, comprises: providing two or more waveguides, calculating segment parameters for segments within a coupling region, said one or more parameters relating to propagation constants of respective waveguides, said one or more parameters being different for said first and second waveguides respectively and thereby providing detuning between said first and second waveguides to allow for unitary operation between said first and second waveguides with high fidelity in the presence of errors, then building the segments into the respective waveguides and optically coupling the waveguides at the coupling region using the segment parameters, thereby to construct a quantum logic gate for a unitary operation.