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Quantum Science and Technology

Entangling distant qubits via flying photons under thermal noise protected by multi-time-bin encoding

Jing Wu, Changqing Wang, Andrew Cameron, Yao Lu, Silvia Zorzetti

Published Oct 2, 2026• 0 citations
Publisher

Abstract

Abstract Entangling distant stationary qubits—such as superconducting qubits, color centers, trapped ions, and phononic modes—commonly relies on flying photons transmitted through noisy channels. The fidelity of remote entanglement is severely degraded by channel noise. While entanglement purification can theoretically mitigate this effect, its practical implementation in quantum networks is limited by the overhead of local operations and classical communication. We propose a multi-time-bin encoding scheme that improves the fidelity of remote entangled stationary qubits without relying on entanglement purification. Our results show that, compared to single-rail (vacuum–one-photon) encoding, the fidelity in thermal-loss Gaussian channels is improved from 0.66 to 0.89. Taking superconducting qubits connected through microwave-to-optical transduction as a representative implementation, the fidelity is increased from 0.75 to 0.98. Finally, we discuss the prospects for extending the protocol to other stationary-qubit platforms.

DOI
10.1088/2058-9565/aeaf81

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Abstract Entangling distant stationary qubits—such as superconducting qubits, color centers, trapped ions, and phononic modes—commonly relies on flying photons transmitted through noisy channels. The fidelity of remote entanglement is severely degraded by channel noise. While entanglement purification can theoretically mitigate this effect, its practical implementation in quantum networks is limited by the overhead of local operations and classical communication. We propose a multi-time-bin encoding scheme that improves the fidelity of remote entangled stationary qubits without relying on entanglement purification. Our results show that, compared to single-rail (vacuum–one-photon) encoding, the fidelity in thermal-loss Gaussian channels is improved from 0.66 to 0.89. Taking superconducting qubits connected through microwave-to-optical transduction as a representative implementation, the fidelity is increased from 0.75 to 0.98. Finally, we discuss the prospects for extending the protocol to other stationary-qubit platforms.
Recent studies have shown long-distance entanglement using NV centers, atoms, and quantum dots with single-photon time-bin encoding. We propose a method to entangle remote superconducting qubits via microwave-optical transduction using multi-time-bin states. By adapting conventional entanglement swapping techniques, fidelity improves from 0.75 to 0.980.980.98 in transduction systems, and 0.66 to 0.89 in noisy channels. The protocol mitigates thermal noise without relying on purification and offers a practical path toward scalable, heterogeneous quantum systems.
We present an efficient strategy for sharing multipartite polarization entanglement between distant locations via the noisy channel assisted by the time-bin degree of freedom. We demonstrate an entanglement purification protocol for the three-qubit Greenberge–Horne–Zeilinger state and an entanglement distribution protocol for the three-qubit W state. We also generalize the protocol to distribute arbitrary N-photon polarization states to N distant locations. Our schemes do not consume a large number of less-entangled systems and the remote parties can share the desired state in a deterministic way with 100% fidelity in principle. These advantages make our method useful and practical in long-distance quantum communication.
Remote entanglement of distant, noninteracting quantum entities is a key primitive for quantum information processing. We present a protocol to remotely entangle two stationary qubits by first entangling them with propagating ancilla qubits and then performing a joint two-qubit measurement on the ancillas. Subsequently, single-qubit measurements are performed on each of the ancillas. We describe two continuous variable implementations of the protocol using propagating microwave modes. The first implementation uses propagating $\mathrm{Schr}\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\mathrm{o}}$ dinger cat states as the flying ancilla qubits, a joint-photon-number-modulo-2 measurement of the propagating modes for the two-qubit measurement, and homodyne detections as the final single-qubit measurements. The presence of inefficiencies in realistic quantum systems limit the success rate of generating high fidelity Bell states. This motivates us to propose a second continuous variable implementation, where we use quantum error correction to suppress the decoherence due to photon loss to first order. To that end, we encode the ancilla qubits in superpositions of Schr\"odinger cat states of a given photon-number parity, use a joint-photon-number-modulo-4 measurement as the two-qubit measurement, and homodyne detections as the final single-qubit measurements. We demonstrate the resilience of our quantum-error-correcting remote entanglement scheme to imperfections. Further, we describe a modification of our error-correcting scheme by incorporating additional individual photon-number-modulo-2 measurements of the ancilla modes to improve the success rate of generating high-fidelity Bell states. Our protocols can be straightforwardly implemented in state-of-the-art superconducting circuit-QED systems.
High-fidelity quantum entanglement is a key resource for quantum communication and distributed quantum computing, enabling quantum state teleportation, dense coding, and quantum encryption. Any sources of decoherence in the communication channel, however, degrade entanglement fidelity, thereby increasing the error rates of entangled state protocols. Entanglement purification provides a method to alleviate these nonidealities by distilling impure states into higher-fidelity entangled states. Here we demonstrate the entanglement purification of Bell pairs shared between two remote superconducting quantum nodes connected by a moderately lossy, 1-meter long superconducting communication cable. We use a purification process to correct the dominant amplitude damping errors caused by transmission through the cable, with fractional increases in fidelity as large as 25%, achieved for higher damping errors. The best final fidelity the purification achieves is 94.09±0.98%. In addition, we use both dynamical decoupling and Rabi driving to protect the entangled states from local noise, increasing the effective qubit dephasing time by a factor of 4, from 3 to 12 μs. These methods demonstrate the potential for the generation and preservation of very high-fidelity entanglement in a superconducting quantum communication network.
Long-distance entanglement distribution is hindered by photon loss in optical fibers and the nocloning theorem. Optical quantum repeater (QR) protocols rely on Bell state measurements (BSMs), they are intrinsically limited to probabilistic photon operations and fail 50% of the time. We propose a hybrid approach to building quantum repeaters that combines the high transmission speed of photonic qubits in optical fiber with the high-fidelity quantum processing capabilities enabled by superconducting circuits. The transduction-enabled superconducting QR (TESQR) architecture eliminates the need for probabilistic BSMs and allows deterministic processing operations. The TESQR framework always yields a final state at the remote nodes rather than aborting on photon loss, manifesting deterministic entanglement distribution within certain parameter regimes. We evaluate the performance by assessing output-state fidelities and success probabilities of entanglement distribution using realistic noise models. Additionally, we integrate an entanglement purification scheme and evaluate the performance through numerical simulations in QuTiP environment. Our results show that, for entanglement swapping, the proposed scheme improves the entanglement distribution rate by an average of 63% and by up to 159% compared with photonic-only architectures. Moreover, after purification, the end-to-end fidelities exceed 0.8 over distances up to 20 km.
One of the most promising ways to transfer quantum information between superconducting qubits is with microwave photons. Enhancing direct quantum channels by time-bin encoding techniques, which map qubit states to single-photon states emitted at different times, allows the detection of photon-loss errors, and thus heralded quantum communication is possible. The authors realize and experimentally benchmark an error-detection scheme that allows them to select only experimental runs in which the photon state was transmitted successfully, yielding significantly improved fidelity of the transfer in this post-selected setting.