Entangling remote qubits through a two-mode squeezed reservoir

The gist The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks, and this paper demonstrates an alternative, fully autonomous process where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir.

Entanglement Distribution Mechanism

The core of the scheme involves driving two separated transmon qubits with the output of a non-degenerate Josephson parametric converter (JPC) [1]. The JPC produces a propagating twomode squeezed (TMS) state of microwave photons [2], which successively relaxes the two frequency-detuned qubits into an entangled steady state [2]. This process relies on an intriguing non-local interference effect that harnesses the preexisting quantum correlations of the distributed photonic state [3]. Under ideal conditions, this scheme can be applied over arbitrary distances and extended to complex, multi-qubit entangled states using only a single correlated photon source [3]. The JPC consists of two stripline-based resonators with frequencies set at 6.761 GHz and 10.044 GHz, coupled by a Josephson ring modulator [2].

Qubit State and Entanglement Certification

The qubits are driven into a pure and almost maximally entangled Bell state, specifically the state Φ⟩ = √N + 1 gg⟩ + e iϕp√N ee⟩/√2N + 1, which approaches a maximally entangled Bell state for N ≳ 1 [2]. This state is verified by showing that the Jaynes-Cummings interaction HJC Φ⟩ ΨTMS⟩ = 0, meaning it is the unique entangled dark state that decouples from the correlated photonic environment [3]. Entanglement certification can be achieved by employing efficient correlation detectors to certify entanglement of a weakly excited TMS microwave state directly at cryogenic temperatures and in a parameter regime where conventional linear detection schemes with noisy pre-amplifiers are inefficient [2].

Experimental Verification and Characterization

The transfer of entanglement from a CV to a DV state is verified by time-resolved qubit measurements, including phase coherence experiments where the joint expectation value is shown to oscillate coherently for ϕp = 0 [3]. Full state tomography is performed using 25 different measurement bases to extract the 16 independent expectation values of the two-qubit subspace, allowing for the reconstruction of the density matrix ρ [3]. The results show excellent agreement between experiment and theory for specific photon transmission parameters ηi = (0.5, 0.3) [3].

Entanglement Quantification and Limits

The paper quantifies entanglement using several measures:

1. Continuous-variable entanglement is characterized by the symplectic eigenvalues ν±, which can be used to calculate the entanglement of formation (EOF) [4].

2. Discrete-variable entanglement is quantified by concurrence C(ρq), defined as max(0, λ1 − λ2 − λ3 − λ4) [14].

3. The maximum achievable concurrence for the bidirectional waveguide case is analytically obtained as C⋆ ≈ 0.258 at an optimal squeezing strength r⋆ ≈ 0.465 [18].

Key Findings and Future Directions

The study demonstrates that about a tenth of the entanglement of formation present in the TMS state is inherited by the qubits, which agrees with theory [3]. The fast stabilization time, approximately 300 ns, is beneficial for further entanglement distillation protocols with high throughput [3]. The work also provides a first calibration-free verification of a two-mode squeezed state in the microwave domain using qubits as both photon and correlation detectors [19]. Future improvements are expected by using higher-purity or broadband squeezing sources and multiplexed protocols to increase the distributed concurrence [18].

How it works

The scheme operates by coupling two spatially separated transmon qubits to a quantum-correlated photonic reservoir generated by a JPC [2]. The JPC produces a Gaussian, continuous-variable entangled state of propagating microwave fields that drives the qubits into a stationary, discrete-variable entangled state [2]. This is achieved through an effective two-mode squeezing Hamiltonian (Eq. 1) for the JPC [2]. The qubits decay symmetrically with rates γL,i = γR,i, and they are separated from the photon source by 50 cm of coaxial cable each [2].

Key Components and Modeling

The experimental setup involves a JPC connected to two transmon qubits via circulators to prevent backaction or direct qubit-qubit interactions via transmission lines [2]. The dynamics are modeled using an effective master equation (Eq. E6) which describes the reduced state of the qubits, incorporating terms for JPC evolution, qubit decay into waveguide modes, and dephasing [2]. The gain-bandwidth relation is defined by δω = κ/√G0 ≈ κ/(P - 1)(1/2), which is experimentally accessible and matches observations in Fig. 3d [2].

Detection Strategies

The paper compares standard amplified heterodyne detection with using qubits as primary detectors, showing that the qubit detection method can yield a two orders of magnitude improvement in single-shot variance for very low photon numbers [15]. The average photon number of the TMS mode Ni is extracted from the qubit expectation value Ni = ξ-1 i Pe i, where Pe i is calculated from the steady-state expectation values [3]. This qubit detection method provides a lower bound and confirms that the two microwave fields are entangled without needing noise subtraction or other calibration techniques [2].

Limitations and Practical Constraints

The main limitations on achievable entanglement arose from bidirectional waveguide couplings, losses in the transmission lines, and unexpectedly large asymmetry in the qubit decay rates [3]. The upper bound for concurrence in the bidirectional scenario is C⋆ ≈ 0.258 at an optimal squeezing strength r⋆ ≈ 0.465 [18]. These issues can be improved by terminating transmission lines, using higher-purity or broadband squeezing sources, and multiplexed protocols [18]. The paper also notes that the observed coherences gg⟩⟨ee clearly exceed the unwanted single-qubit diagonal elements due to photon loss and other factors [3].

Conclusion

In summary, this work presents the first experimental realization of qubit-qubit entanglement distribution through a correlated photonic reservoir [1]. The demonstration of fast stabilization time and calibration-free verification of a two-mode squeezed state in the microwave domain opens up new avenues for high-throughput entanglement distribution and quantum technological applications [3].

--- Page 1 ---

The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks, and this paper demonstrates an alternative, fully autonomous process where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir.

The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks, and this paper demonstrates an alternative, fully autonomous process where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir.

The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks, and this paper demonstrates an alternative, fully autonomous process where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir.

The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks, and this paper demonstrates an alternative, fully autonomous process where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir.

The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks, and this paper demonstrates an alternative, fully autonomous process where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir.

The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks, and this paper demonstrates an alternative, fully autonomous process where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir.

The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks, and this paper demonstrates an alternative, fully autonomous process where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir.

The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks, and this paper demonstrates an alternative, fully autonomous process where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir.</ref:2510.

1. Continuous-Variable Entanglement Distribution via CV-DV Hybrid Schemes: The system can distribute entanglement across distant qubits by coupling them to a quantum-correlated photonic reservoir, allowing the distribution and transfer between CV and DV entanglement realized in this work to be achieved autonomously, overcoming the mismatch between readily available CV states and practically useful DV systems.

2. Direct Certification of Squeezing: Superconducting qubits can be used to directly certify two-mode squeezing, with higher sensitivity and without the need for calibrated noise-subtraction, enabling real-time monitoring of quantum resource quality at cryogenic temperatures.

3. Calibration-Free State Verification: The system enables the first calibration-free verification of a two-mode squeezed state in the microwave domain by using qubits as both photon and correlation detectors, which is crucial for scalable, low-overhead quantum networks.

4. High-Throughput Entanglement Distribution: The demonstrated fast stabilization time allows for the realization of high-throughput and low control-complexity entanglement distribution, supporting large-scale quantum communication protocols.

5. Entanglement Quantification in CV Channels: The system can quantify continuous variables using metrics like the Entanglement of Formation (EF), which is calculated based on symplectic eigenvalues, providing a rigorous measure of entanglement for the propagating reservoir state.

6. Bidirectional Channel Modeling: Theoretical analysis allows for calculating the maximally achievable concurrence C⋆ under bidirectional waveguide coupling, establishing an upper bound for entanglement that can be used to design optimal network topologies.

7. Robust Entanglement Stabilization: By utilizing mechanisms like tunable couplers to turn off the coupling between qubit and waveguide, the system can protect entangled states from decay, extending coherence times beyond the intrinsic qubit relaxation time.