Nonlinear elements can efficiently implement quantum information processing systems such as controlled phase shifters, non-absorbing detectors including parity detectors, quantum subspace projections, non-absorbing Bell state analyzers, non-absorbing encoders/entanglers, and fundamental quantum gates such as CNOT gates. The non-absorbing detectors permit improvements in the efficiency of a probabilistic quantum gate by permitting reuse of the same photonic resources during multiple passes through the probabilistic gate.