Remote Preparation of Single-Photon “Hybrid” Entangled and Vector-Polarization States

Quantum teleportation faces increasingly demanding requirements for transmitting large or even entangled systems. However, knowledge of the state to be transmitted eases its reconstruction, resulting in a protocol known as remote state preparation. A number of experimental demonstrations to date have been restricted to single-qubit systems. We report the remote preparation of two-qubit “hybrid” entangled states, including a family of vector-polarization beams. Our single-photon states are encoded in the photon spin and orbital angular momentum. We reconstruct the states by spin-orbit state tomography and transverse polarization tomography. The high fidelities achieved for the vector-polarization states opens the door to optimal coupling of down-converted photons to other physical systems, such as an atom, as required for scalable quantum networks, or plasmons in photonic nanostructures.

Figure 1

Experimental setup for the remote preparation of single-photon entangled and vector-polarization states. LC, liquid crystals (LC1 for state preparation, LC2 for polarization tomography) with optic axis perpendicular to the beam and oriented as indicated (+, ×); BSA, Bell-state analyzer; QWP, quarter-wave plate; HWP, half-wave plate; SMF, single-mode fiber; APD, avalanche photodiode; PBS, polarizing beam splitter; holo, forked binary-grating hologram; tomo holo, holograms for spatial-mode tomography [22].

Figure 2

Experimental density matrices (real parts) of remotely prepared single-photon two-qubit states. (a)–(d) Maximally entangled spin-orbit states, (e),(f) partially mixed states, and (g) completely mixed state. Family of vector-polarization states, (h)–(k), with their ideal polarization profiles shown underneath [spatial-mode component of the density matrix shown in the basis $|h/v⟩=(|l⟩\pm |r⟩)/\sqrt{2}$]. The average magnitude of all imaginary elements, not shown, is 0.02.

Figure 3

Transverse polarization and intensity profiles of remotely prepared vector beams. For a canonical maximally entangled spin-orbit state ${\varphi }^{-}\equiv \frac{1}{\sqrt{2}}(|Hl⟩-|Vr⟩)$, we show (a) the intensity profiles for each polarization projection and (b) the polarization profiles from state tomography at each point; the average fidelity with the target states over all sampled points is $F_{\mathrm{av}}=95(4)\%$. (c) Radial polarization, $F_{\mathrm{av}}=94(4)\%$, and (d) azimuthal polarization, $F_{\mathrm{av}}=95(2)\%$. The polarization ellipses are shown for a subset of all samples, and their size suggests the magnitude of state purity, where pure states have the size of the colored circles (equivalent to the size of the collection pinhole).