Quantum teleportation over thermal microwave network

Abstract

Quantum communication in the microwave regime is set to play an important role in distributed quantum computing and hybrid quantum networks. However, typical superconducting quantum circuits require millikelvin temperatures for operation, which poses a significant challenge for largescale microwave quantum networks. Here, we present a solution to this challenge by demonstrating the successful quantum teleportation of microwave coherent states between two spatially-separated dilution refrigerators over a thermal microwave channel in the temperature range up to $4$ K. We distribute two-mode squeezed states over this noisy channel and employ the resulting quantum entanglement for quantum teleportation of coherent states with fidelities of $72.3 \pm 0.5 ~\%$ at $1$ K and $59.9 \pm 2.5 \%$ at $4$ K, exceeding the no-cloning and classical communication thresholds, respectively. We successfully model the teleportation protocol using a Gaussian operator formalism that includes losses and noise. Our analysis shows that the teleportation infidelity mainly stems from a parasitic heating of the cold quantum nodes due to the hot network connection. These results demonstrate the experimental feasibility of distributed superconducting architectures and motivate further investigations of noisy quantum networks in various frequency regimes.

Figures (4)

• Figure 1: Cryolink and experimental setup. (a) Schematic of the cryolink connecting Alice and Bob, including a cross-sectional view of the MC tube at the cryolink center. (b) Schematic representation of the coherent quantum teleportation protocol with an analog feedforward. Schematics of (c) the TMS state generation, (d) the feedforward generation with a Josephson interferometer, and (e) Bob's local displacement operation.
• Figure 2: Quantum teleportation between distant dilution refrigerators. (a) Negativity $N$ and purity $\mu$ of TMS states distributed over the cryolink for various squeezing levels $S_\textrm{TMS}$. The vertical dashed line indicates the chosen operating point of $S_\textrm{TMS}=5dB$. (b) Teleported state fidelities $F$ of "quantum" and "classical" teleportation protocols as a function of the input state photon number $n_\textrm{in}$ and averaged across displacement angles. Solid lines represent fits using our theoretical model. Gray- and blue-shaded regions indicate fidelities below the classical $F_\textrm{cl}$ and no-cloning $F_\textrm{nc}$ thresholds, respectively. (c) Exemplary Wigner functions of relevant coherent states. Yellow and green dashed lines denote the $1/e$ Gaussian contours of the input and teleported states, respectively. Error bars denote the standard error of the experimental data and are smaller than the symbol size when not shown.
• Figure 3: Entanglement distribution through the 4K thermal channel. (a) Average temperatures $T$ of various MC sections as a function of the cryolink center temperature $T_\textrm{cen}$. (b) Negativity $N$ and purity $\mu$ of the TMS states as a function of $T_\textrm{cen}$. Error bars denote the standard error of the experimental data and are smaller than the symbol size when not shown.
• Figure 4: Quantum teleportation through the 4K thermal channel. (a) Teleported state fidelities $F$ of "quantum" and "classical" teleportation for various $T_\textrm{cen}$. Solid lines represent fits using our theoretical model. Gray- and blue-shaded regions indicate fidelities below the classical $F_\textrm{cl}$ and no-cloning $F_\textrm{nc}$ thresholds, respectively. Purple dash-dotted and dashed lines represent predicted qubit state teleportation fidelities for $S_\textrm{TMS}=5dB$ and $S_\textrm{TMS}=10dB$, respectively. (b) Wigner functions of exemplary teleported coherent states. Yellow and green dashed lines denote the $1/e$ contours of the input and teleported states, respectively. Error bars denote the standard error of the experimental data and are smaller than the symbol size when not shown.