Fully controllable time-bin entangled states distributed over 100-km single-mode fibers

Quantum networks that can perform user-defined protocols beyond quantum key distribution will require fully controllable entangled quantum states. To expand the available space of generated time-bin entangled states, we demonstrate a time-bin entangled photon source that produces qubit states \(|{\psi}\rangle = \alpha |{00}\rangle + \beta |{11}\rangle \) with fully controllable phase and amplitudes. Eight different two-photon states have been selected and prepared from arbitrary states on the reduced two-qubit Bloch sphere. The photon pairs encoded in the time-bin scheme were generated at 2.4 MHz with a visibility of \(V = 0.9475 \pm 0.0016\), with a violation of the CHSH Bell’s inequality by 197 standard deviations. After entanglement distribution over 100 km of single-mode fibers, we obtained a visibility of \(V = 0.9541 \pm 0.0113\) with a violation of the CHSH Bell’s inequality by 6 standard deviations. The prepared states had an average fidelity of \(0.9540 \pm 0.0016\) at the source and an average fidelity of \(0.9353 ^{+0.0100}_{-0.0209}\) after entanglement distribution, which shows that the quantum states generated by our time-bin entangled photon source can be fully controlled potentially to a level applicable to long-distance advanced quantum network systems.