Gigahertz-Clocked Teleportation of Time-Bin Qubits with a Quantum Dot in the Telecommunication $C$ Band

Teleportation is a fundamental concept of quantum mechanics with an important application in extending the range of quantum communication channels via quantum relay nodes. To be compatible with real-world technology such as secure quantum key distribution over fiber networks, such a relay node should ideally operate at gigahertz clock rates and accept time-bin-encoded qubits in the low-loss telecom band around 1550 nm. Here, we show that $\mathrm{In}\mathrm{As}$-$\mathrm{In}\mathrm{P}$ droplet-epitaxy quantum dots, with their sub-Poissonian emission near 1550 nm, are ideally suited for the realization of this technology. To create the necessary on-demand photon emission at gigahertz clock rates, we develop a flexible-pulsed optical-excitation scheme and demonstrate that the fast driving conditions are compatible with a low multiphoton emission rate. We show further that, even under these driving conditions, photon pairs obtained from the biexciton cascade show an entanglement fidelity close to 90%, comparable to the value obtained under continuous-wave excitation. Using asymmetric Mach-Zehnder interferometers and our photon source, we finally construct a time-bin qubit quantum relay able to receive and send time-bin-encoded photons and demonstrate mean teleportation fidelities of $0.82\pm 0.01$, exceeding the classical limit by more than ten standard deviations.

Figure 1

Interfacing gigahertz-clocked time-bin qubits with a quantum-dot relay. Alice produces a gigahertz-clocked time-bin-encoded qubit by sending polarization-encoded weak coherent pulses through an interferometric transcoding unit. Subsequent time-encoded photons are then sent to a relay node, Charlie, where upon conversion back into polarization encoding using a phase-stabilized second transcoding unit, the state can be teleported using a gigahertz-clocked polarization-entangled photon-pair source. After successful teleportation at Charlie, photons can again be transcoded to time-bin encoding before being sent on to a receiver, Bob. P, polarization qubit; TB, time-bin qubit; T1–T3, transcoder units; A, time-bin qubit analysis; BSM, Bell-state measurement; E, entnalged photon pairs.

Figure 2

The gigahertz-clocked emission from a QD emitting near the telecom $C$ band. (a) A schematic of the excitation setup. A 1310-nm cw laser is modulated by an EOM with active voltage stabilization in order to create flexible excitation pulses. The gigahertz-clocked emission is collected from the QD and sent to the detection system, where time-resolved measurements can be made using the excitation clock from the pulse generator: PC, polarization controller; EOM, electro-optic modulator; BS, beam splitter; PD, photodiode; DM, dichroic mirror; FC, fiber coupler; DVA, digital variable attenuator; TG, transmission grating; SNSPDs, superconducting-nanowire single-photon detectors. The inset shows the spectrum of the QD measured under pulsed excitation at a power where the exciton intensity begins to saturate. The emission lines of the exciton ($X$) and the biexciton ($XX$) are labelled. (b) The second-order intensity correlations of the $X$ for 100-MHz (top) and 1.07-GHz (bottom) excitation frequencies. The solid lines show fits to the data. (c) The time-resolved intensity of the $X$ and the $XX$ emission lines at a repetition frequency of 100 MHz (top) and 1.07 GHz (bottom). (d) The second-order correlation of the $X$ photons, measured with respect to the excitation laser clock. The data binned on a $40\times 40$ ps grid show a leading diagonal of empty photon counts corresponding to the low probability of finding two $X$ photons emitted in the same clock cycle. The color bar denotes normalized coincidences.

Figure 3

The degree of entanglement under gigahertz-clocked excitation. (a) The real (left) and imaginary (right) parts of the two-photon density matrix, reconstructed using a time window of 96 ps, under pulsed optical excitation clocked at 1.07 GHz. (b) The evolution of the fidelity of the two-photon state to the ${\mathrm{\Phi }}^{+}$ Bell state and a maximally entangled state, calculated from the two-photon density matrix for different 96-ps time windows. (c) A comparison of the maximum fidelity to the ${\mathrm{\Phi }}^{+}$ Bell state for different driving frequencies (see text for details).

Figure 4

Superposition-basis teleportation at 1 GHz. (a) Input laser qubits in the time-bin basis for a superposition state (left) and an early state (right). (b) A schematic of the polarization-basis relay station where a time-bin input laser qubit is sent through a transcoder unit (TU) before being teleported using an entangled photon pair generated from the QD. Other optical elements are as defined in Fig. 2. (c) The normalized third-order correlations for sending input laser qubits in a superposition of $|e⟩$ and $|l⟩$ time bins, which is subsequently mapped to an $|A⟩$-polarized photon, and measuring $|A⟩$- (left) and $|D⟩$- (right) polarized photons at Bob. (d) The teleportation fidelities for a complete set of orthogonal input states, calculated from the third-order correlations centered on the time $t_{\mathrm{Bob}}=t_{\mathrm{Charlie}}=0$, the point at which all three photons are measured simultaneously. The results for the most statistically significant equivalent postselection window size of 228 ps are shown. Each state surpasses the classical threshold of $2/3$ and a mean fidelity of $0.82\pm 0.01$ beats this limit by more than 10 $\sigma$.

Figure 5

Time-bin logical-basis teleportation. (a) The normalized third-order correlations for sending input laser qubits in $|e⟩$ and $|l⟩$ time bins, which are subsequently mapped to $|l⟩$ and $|e⟩$ time bins after sending Bob’s photons back through the interferometer. (b) The teleportation fidelities along $t_{\mathrm{Charlie}}=0$, showing that input $|e⟩$ is mapped to $|l⟩$, corresponding to the polarization mapping of $|H⟩$ to $|V⟩$ in the teleportation.