Programmable heralded linear optical generation of two-qubit states
Suren A. Fldzhyan, M. Yu. Saygin, S. P. Kulik · Physical Review Applied · 2023
We investigated the heralded generation of two-qubit dual-rail-encoded states by programmable linear optics. Two types of scheme generating the states from four single photons, which is the minimum possible to accomplish the task, were considered. The schemes have different detection patterns heralding successful generation events; namely, one-mode heralding, in which the two auxiliary photons are detected in one mode, and two-mode heralding, in which single photons are detected in each of the two modes simultaneously. We show that the dependencies of the schemes' success probabilities on the target state's degree of entanglement are essentially different. In particular, one-mode heralding yields greater efficiency for highly entangled states if the programmable interferometers can explore the full space of the unitary transfer matrices. The reverse is the case for weakly entangled states, where two-mode heralding is better. We found a minimal decomposition of the scheme with two-mode heralding that is programmed by one variable phase shift. We infer that the linear optical schemes designed specifically for the generation of two-qubit states are more efficient than schemes implementing known linear optical gate--based circuits. Our results reveal a substantial reduction of physical resources needed to generate some types of nonmaximally entangled multiqubit states used in quantum computing.