Autonomous stabilization of remote entanglement in a cascaded quantum network

Remote entanglement between widely separated qubits is a fundamental quantum phenomenon and a critical resource for quantum information applications. Generating entanglement between independent qubits separated by arbitrary, potentially large distances requires propagating quantum states, and is typically achieved using pulsed protocols combining distinct steps of local entanglement generation followed by distribution. This necessity raises an intriguing question: Can remote entanglement be stabilized indefinitely, instead of only periodically regenerated and redistributed after decay? Here, we demonstrate that this is indeed possible, reporting autonomous stabilization of entanglement between two separate superconducting-qubit devices. Combining nonreciprocal waveguide coupling and local driving, we experimentally realize a symmetry-based coherent quantum-absorber scheme in a cascaded network. We quantify the degree of entanglement through quantum state tomography, finding that the protocol’s entangling power is severely limited by imperfections that break the required symmetry. We show, however, that a modified protocol based on an alternate symmetry is far more robust, enabling us to achieve a concurrence approaching 0.5, a limit set only by local loss in the network. Our results enable on-demand delivery of high-fidelity entanglement in modular quantum processors and networks and pave the way for autonomously protecting distributed quantum information.

💡 Research Summary

The paper addresses a fundamental challenge in quantum information processing: how to maintain entanglement between spatially separated qubits indefinitely, without the need for periodic re‑preparation. Conventional approaches generate entanglement locally and then distribute it using pulsed protocols; the resulting state inevitably decays due to decoherence and must be regenerated. The authors propose and experimentally demonstrate an autonomous, steady‑state stabilization scheme that continuously supplies the required non‑local dissipation and coherent drive, thereby making the entangled state the unique non‑equilibrium fixed point of the dynamics.

The theoretical backbone is the “coherent quantum absorber” (CQA) protocol. Two superconducting transmon qubits (labeled Alice and Bob) are coupled radiatively to a unidirectional waveguide with rates γA and γB. In the ideal symmetric case (γA = γB ≡ γ) and with identical Rabi drives ΩA = ΩB ≡ Ω applied at the same frequency (detuning ε = 0), the cascade interaction causes the emission from the upstream qubit to be perfectly absorbed by the downstream qubit. Destructive interference of the emitted photons creates a dark state |ψ⟩ ∝ |00⟩ + α(|01⟩ − |10⟩), where α = √2 Ω/(2Δ − iγ). For large Ω the state approaches the maximally entangled singlet (|01⟩ − |10⟩)/√2. In this picture the entangled state is a steady state of the combined driven‑dissipative dynamics, independent of the physical distance between the qubits.

Experimentally the authors realize a low‑loss cascaded network. Two fixed‑frequency transmons are housed in waveguide‑compatible enclosures and linked by ~60 cm of low‑loss coaxial cable together with a microwave circulator that enforces unidirectional propagation. Measured relaxation rates give γA/2π ≈ 0.53 MHz and γB/2π ≈ 1.22 MHz, close to the target 1 MHz. A separate scattering experiment yields a transmission efficiency η² = 0.96 ± 0.01, confirming that the waveguide introduces only minimal loss.

Applying the symmetric CQA protocol, the authors sweep the drive amplitude Ω while keeping ΩA = ΩB and ε = 0. Concurrence rises from zero at small Ω, reaches a modest maximum (~0.2) around Ω/2π ≈ 12 MHz, and then declines for larger Ω. The limited performance is traced to unavoidable asymmetries: γA ≠ γB, slight mismatches in ΩA and ΩB, and residual local decoherence (T₁, T₂). These imperfections break the exchange symmetry that the original CQA theory assumes, preventing the formation of the ideal dark state.

To overcome this, the authors identify an alternative symmetry that does not require exact matching of the two qubits. By deliberately detuning the drives (ε ≠ 0) and allowing ΩA ≠ ΩB, they engineer a different dark state that mimics two‑mode squeezing. In this “modified protocol” the correlated dissipation still dominates, but the steady‑state condition becomes tolerant to the measured asymmetries. With appropriately chosen parameters the concurrence climbs to C ≈ 0.48, essentially limited only by the measured waveguide loss (η) and the intrinsic local relaxation of the transmons.

A further technical hurdle is the short T₁ of the qubits (≈300 ns for Alice, 130 ns for Bob), which makes conventional single‑shot readout infeasible. The authors therefore employ a calibrated positive‑operator‑valued‑measure (POVM) tomography: they simulate the relaxation dynamics during the pre‑rotation pulses, incorporate this into the measurement operators, and reconstruct the two‑qubit density matrix via convex optimization. This method yields reliable estimates of all two‑qubit correlators ⟨σ_i⊗σ_j⟩ and the concurrence, with uncertainties quantified in the supplementary material.

Overall, the work demonstrates that autonomous steady‑state entanglement between remote superconducting qubits is experimentally viable, provided that the engineered non‑local dissipation dominates over local loss and that the protocol is robust to realistic asymmetries. The modified symmetry approach offers a practical pathway to higher‑fidelity entanglement without demanding perfect device matching. The results open the door to on‑demand delivery of entangled resources in modular quantum processors, quantum repeaters, and distributed quantum computing architectures, and they suggest that further reductions in local loss and improvements in waveguide engineering could push the steady‑state concurrence toward the theoretical limit of 0.5.