Real-time imaging of spin-to-orbital angular momentum hybrid remote state preparation

There exists two prominent methods to transfer information between two spatially separated parties, namely Alice (A) and Bob (B): quantum teleportation and remote state preparation. However, the difference between these methods is, in the teleportation scheme, the state to be transferred is completely unknown, whereas in state preparation it should be known to the sender. In addition, photonic state teleportation is probabilistic due to the impossibility of performing a two-particle complete Bell-state analysis with linear optics, while remote state preparation can be performed deterministically. Here we report the first realization of photonic hybrid remote state preparation from spin to orbital angular momentum degrees of freedom. In our scheme, the polarization state of photon A is transferred to orbital angular momentum of photon B. The prepared states are visualized in real time by means of an intensified CCD camera. The quality of the prepared states is verified by performing quantum state tomography, which confirms an average fidelity higher than 99.4%. We believe that this experiment paves the way towards a novel means of quantum communication in which encryption and decryption are carried out in naturally different Hilbert spaces, and therefore may provide a means for enhancing security.

Figure 1

Quasi-cw 150 mW UV laser (355 nm, repetition rate 100 MHz, ${\text{TEM}}_{00}$ mode) pumps a phase-matched, type-I BBO crystal. The generated photon pairs are entangled in their OAM DOF. Charlie controls the orientations of the QWP (Q) and HWP (H), which allows him to place photon A in an arbitrary polarization state. The polarizing Sagnac interferometer containing a Dove prism (PSI-DP), shown in the inset, in combination with the HWP, spatial light modulator (SLM), bandpass interference filter (IF), and single mode optical fiber (SMF) perform the Bell-state measurement [20]. The HoloEye Pluto SLM diffracts only horizontally polarized photons, acting as a polarizer. An SLM with a proper hologram and a SMF postselect the OAM Hilbert subspace: only photons with a flattened wavefront $\left(\left|\ell \right|=0\right)$ can propagate efficiently through an SMF. The photons couple via a fiber coupler (FC) into the SMF for detection by an avalanche photon diode (APD). The detector (APD) triggers the ICCD camera to record the spatial distribution of photon B. Photons are filtered with 10 nm IFs before the detector and ICCD camera for noise reduction. During the preparation and measurement of photon A, photon B propagates in delay line (D), compensating for electronic delay. To measure the fidelity of the transported state, the ICCD camera is replaced by another SLM and the coincidence counts between A's and B's detectors are measured.

Figure 2

Qualitative comparison of experimental data and theoretical predictions. (a) Pictorial representation of the prepared states on the OAM Poincaré sphere. South and north poles represent the $\left|+\ell \right.〉$ and $\left|-\ell \right.〉$-states, respectively, and an equal superposition of $\left|+\ell \right.〉$ and $\left|-\ell \right.〉$ stands on the equator. (b) Theoretically predicted spatial distributions of the prepared states corresponding to initial polarization states of Charlie being set to circular-left $\left|L\right.〉\to \left|\ell \right.〉$, horizontal $\left|H\right.〉\to \left|h_{\ell }\right.〉$, antidiagonal $\left|A\right.〉\to \left|a_{\ell }\right.〉$, vertical $\left|V\right.〉\to \left|v_{\ell }\right.〉$, and diagonal $\left|D\right.〉\to \left|d_{\ell }\right.〉$. (c) Experimentally recorded spatial distributions of photon B on the ICCD camera conditioned by detecting photon A in the spin-orbit Bell state of $\left|{\mathrm{\Phi }}_{\ell }^{+}\right.〉$. Total exposure time per picture is 600 s with a time window of 4 ns.

Figure 3

Real (upper row) and imaginary (lower row) parts of the reconstructed density matrices for the prepared states in OAM subspace of $\left|\ell \right|=2$ shown in Fig. 2. The density matrices are reconstructed via quantum state tomography, where projections over six eigenstates of Pauli matrices are used to estimate the four real parameters that specify the density matrix.