Entangling remote qubits through a two-mode squeezed reservoir

Abstract

The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks. Existing approaches rely on deterministic state transfer schemes or probabilistic protocols that require active control or measurement and postselection. Here we demonstrate an alternative, fully autonomous process, where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir. In our experiment, a Josephson parametric converter produces a Gaussian, continuous-variable entangled state of propagating microwave fields that drives two spatially separated superconducting transmon qubits into a stationary, discrete-variable entangled state. Beyond entanglement distribution, we also show that superconducting qubits can be used to directly certify two-mode squeezing, with higher sensitivity and without the need for calibrated noise-subtraction. These results establish networks of qubits interfaced with distributed continuous-variable entangled states as a powerful new platform for both foundational studies and quantum-technology relevant applications.

Figures (13)

• Figure 1: Sketch of the implemented entanglement distribution scheme. A JPC generates a TMS state (left box: Wigner representation of the microwave field. Dashed circle indicates the vacuum level) that propagates in a cascaded configuration to two distant qubits (blue and red shaded circles). Driven by these correlated fields, the qubits relax into the maximally entangled Bell state $\ket{\Phi^+}$ (right box: density matrix elements of the joint qubit state) and are read out dispersively via separate resonators (not shown).
• Figure 2: Phase coherence and qubit tomography.a, Pulse sequence for the pump phase sweep experiment. Phase-controlled JPC pump pulse (violet), qubit control pulses sent through the resonators (red and blue) controlling the measurement axis $\phi$, and qubit readout pulses (yellow) applied to the readout resonators are shown. b, The measured expectation values of the single and two-qubit operators (see legend) are shown as a function of the qubit 2 measurement axis $\phi$. Lines are fits to a cosine function. c, The same joint expectation value as a function of the phase of the applied JPC pump, $\phi_{\rm p}$. The inset depicts the orientation of the measurement axis. d, Pulse sequence for the qubit tomography experiment implementing 25 different measurement bases for a fixed pump phase. e, Averaged measured expectation values $\langle\sigma_1^i \sigma_2^j\rangle$ and f, real part of the reconstructed 2-qubit density matrix $\rho$ for a pump drive of amplitude $\epsilon_{\rm p}^\star = 0.25$ (yellow bars). Error bars show the $1\sigma$ standard error from 7 repetitions with $10^7$ averages each. Solid frames correspond to the theory model (see Appendix \ref{['app: theory']}).
• Figure 3: Qubit entanglement characterization.a, Measured real part of the reconstructed density matrix elements $\rho_{ij}$ (see legend in panel b), concurrence $\mathcal{C}$, and purity $\mu$ for different squeezing amplitudes $\epsilon_{\rm p}$ and b, different duration of the pump pulse $t_{\rm pulse}$. Error bars show the 1$\sigma$ standard error from 7 (panel a) and 10 (panel b) repetitions with $10^7$ averages each. The solid lines correspond to the theory model. c, Frequency diagram of the detuning experiment. The two qubits at $\omega_{\mathrm{q}, i}$ are detuned from the center frequencies of the respective TMS modes $\omega_{i}$ by $\delta$, maintaining $\omega_{\rm q,1} + \omega_{\rm q,2} = \omega_{\rm p}$. d, Measured concurrence $\mathcal{C}$ as a function of qubit detuning $\delta$ and a Lorentzian fit with a bandwidth $\delta \omega/2\pi=44\MHz$ (solid line). Error bars show the 1$\sigma$ standard error from 3 repetitions with $10^7$ averages each.
• Figure 4: Photonic characterization and entanglement transfer.a-c, Average expectation values of the characteristic photon numbers $N_1, M$ and $N_2$ of the TMS state extracted from calibrated linear detection (black triangles) and the measured qubit expectation values (colored circles). Insets show a zoom of the parameter regime where both methods agree. The data is extracted from raw measurements, that is why in the event of noise for qubit 2, $N_2$ can show negative values. d, Measurements of two-mode squeezing where $\Delta_{\mathrm{EPR}}^- <1$ indicates non-separability. Purple data is taken from direct qubit measurements and gray data from calibrated heterodyne detection, as shown in panels (a-c). e, Entanglement of formation calculated for the TMS state (grey triangles, left axis) and the joint qubit state (orange circles, right axis). Solid lines are calculated based on the ideal squeezing Hamiltonian model from Eq. \ref{['eq:HJPC']} (grey) and the theory model for the full network, also used in Fig. \ref{['fig:3']} (yellow). Error bars show the $1\sigma$ standard error from 7 (5) repetitions with $10^7$ ($2\times10^6$) averages for qubit (linear, 500 kHz) detection.
• Figure 5: Experimental setup. Cryogenic and room temperature experimental setup together with a CAD image of the qubit chip. A detailed explanation is found in the legend and main text.