Free-Space Quantum Key Distribution by Rotation-Invariant Twisted Photons

“Twisted photons” are photons carrying a well-defined nonzero value of orbital angular momentum (OAM). The associated optical wave exhibits a helical shape of the wavefront (hence the name) and an optical vortex at the beam axis. The OAM of light is attracting a growing interest for its potential in photonic applications ranging from particle manipulation, microscopy, and nanotechnologies to fundamental tests of quantum mechanics, classical data multiplexing, and quantum communication. Hitherto, however, all results obtained with optical OAM were limited to laboratory scale. Here, we report the experimental demonstration of a link for free-space quantum communication with OAM operating over a distance of 210 m. Our method exploits OAM in combination with optical polarization to encode the information in rotation-invariant photonic states, so as to guarantee full independence of the communication from the local reference frames of the transmitting and receiving units. In particular, we implement quantum key distribution, a protocol exploiting the features of quantum mechanics to guarantee unconditional security in cryptographic communication, demonstrating error-rate performances that are fully compatible with real-world application requirements. Our results extend previous achievements of OAM-based quantum communication by over 2 orders of magnitude in the link scale, providing an important step forward in achieving the vision of a worldwide quantum network.

Figure 1

Experimental setup. Top image: The experimental layout inside the Venice Lagoon Model Hall located in Padua. Alice’s telescope is on the left, and Bob’s is the one on the far right. The beam profile versus propagation distance $z$ from the telescope is shown in square frames, all having the same side length of 60 mm. Bottom image: Alice’s and Bob’s setups. $L$, $R$, $V$, and $H$ are four attenuated lasers that generate the polarization qubits, calibrated by using a SPAD. Before starting the QKD, a PC is used to impose the correct transfer of the polarization states to the telescope by an optical fiber. On the telescope front focal plane, the polarization qubits are transformed by the $q$-plate into hybrid polarization-OAM qubits and sent toward the receiver. At Bob’s terminal, the beam is gathered by a $15\times$ beam compressor and sent to the second $q$-plate. Here, the hybrid polarization-OAM qubits are transformed back into polarization ones, which are then coupled into a single-mode fiber for spatial-mode filtering and transferred to the Bennett-Brassard 1984 protocol state analyzer.

Figure 2

Experimental QBER and gain. We show the experimental QBER and gain of the signal state $\mu$ (and their statistical errors) at zero rotation angle for each block of 2880 raw bit data. The data show 10 min of acquisition. Dashed lines represent mean values $E_{\mu }=3.81\%$ and $Q_{\mu }=1.41\times {10}^{-2}$ used for the key-rate evaluation, while 0.06% and $0.01\times {10}^{-2}$ represent the errors on the mean values. QBER and gain fluctuations from block to block are due to transmission fluctuation caused by the channel turbulence and to the finite size of the blocks.

Figure 3

Mean QBER. We show the QBERs obtained for the signal state $\mu$ at four different rotation angles of the transmitter device 0°, 15°, 45°, and 60°. The mean QBERs are evaluated over ${10}^5$ sifted bits, and their statistical errors are below 0.1%. The dashed line represents the upper limit of the QBER allowing a positive key rate in the infinite key limit with true single-photon sources, namely, 11%. The continuous red line represents the theoretical QBER that would be obtained by standard polarization encoding, using the polarization states $|H⟩$, $|V⟩$, $|L⟩$, and $|R⟩$.

Figure 4

Secret key rates at different angles. Secret key rates obtained with the decoy state method (red bars or light gray) and corresponding key rates achievable with true single-photon sources (blue bars or dark gray).