Fig. 2: Experimental setup for remote state preparation (RSP).

A CW diode laser emits a 405 nm beam with a power of 1 mW into a polarization Sagnac interferometer (PSI) consisting of a periodically polled KTP (ppKTP) crystal, a dual-wavelength polarizing beam splitter (dPBS, 405/810 nm), a dual-wavelength half-wave plate (dHWP) set at π/4, and two mirrors. The horizontal-polarization beam bidirectionally pumps the ppKTP crystal. A type-II down-conversion in each direction generates two orthogonal polarization photons with a wavelength of 810 nm. When the two oppositely propagating photon pairs coherently interfere at dPBS, the joint state of the photon in mode A and photon in mode B becomes a superposition of the states \({\left\vert H\right\rangle }_{A}{\left\vert V\right\rangle }_{B}\) and \({\left\vert V\right\rangle }_{A}{\left\vert H\right\rangle }_{B}\). By properly setting the angle of the HWP (405 nm) and rotating the quarter-wave plate (QWP, 405 nm) for the input pump, the photon pairs generated from the PSI are close to the target state \(\left\vert {\Psi }^{-}\right\rangle\), where the logical qubit is encoded as \({\left\vert H\right\rangle }_{k}\equiv {\left\vert 0\right\rangle }_{3}\) and \({\left\vert V\right\rangle }_{k}\equiv {\left\vert 1\right\rangle }_{3}\), for the horizontal (H) and vertical (V) polarization states of mode k, respectively. The photon pairs are analyzed using the HWP, QWP, and PBS and are then collected by couplers with narrowband filters (BFs) and long-pass filters (LPFs) for subsequent detection by single photon counting modules (not shown). Alice’s operation U^† = R^†(ϕ) and Bob’s correction operations are implemented by a HWP and two QWPs, respectively (see the Methods and Supplementary Note 2).