Long-distance quantum communication necessitates the use of quantum repeaters, which typically include highly coherent quantum memories. We provide a theoretical analysis of the secret key rates for a quantum repeater system incorporating bosonic error correction and memory components. Specifically, we focus on the application of Binomial codes for two repeater segments. Using these codes, our investigation aims to suppress memory loss errors that commonly affect systems such as atoms and microwave cavities, in contrast to dephasing errors in single-spin memories. We further discuss a physical implementation of such a quantum repeater comprising a microwave cavity and a superconducting transmon, capable of state engineering with high fidelities ($>97\%$) and logical Bell state measurements for successful entanglement swapping. As an alternative approach, we also discuss a realization in the all-optical domain.
Long-distance quantum communication necessitates the use of quantum repeaters, which typically include highly coherent quantum memories. We provide a theoretical analysis of the secret key rates for a quantum repeater system incorporating bosonic error correction and memory components. Specifically, we focus on the application of Binomial codes for two repeater segments. Using these codes, our investigation aims to suppress memory loss errors that commonly affect systems such as atoms and microwave cavities, in contrast to dephasing errors in single-spin memories. We further discuss a physical implementation of such a quantum repeater comprising a microwave cavity and a superconducting transmon, capable of state engineering with high fidelities (>97%) and logical Bell state measurements for successful entanglement swapping. As an alternative approach, we also discuss a realization in the all-optical domain.
In autonomous quantum error correction the lifetime of a logical bosonic qubit can be extended beyond its physical constituents without feedback measurements. Leveraging autonomous error correction, we propose a gate-based microwave quantum repeater (GBMQR) with encoded bosonic grid states. Each repeater station comprises a transmon and two bosonic resonators: one resonator serving as a stationary quantum memory utilizing autonomous error correction, and the other as an information bus for entanglement generation. Entanglement is generated sequentially through the successful absorption of a microwave photon wavepacket. This method enables deterministic entanglement generation, in contrast to a probabilistic mixing of two heralding signals on a balanced beamsplitter. Furthermore, our GBMQR employs an all-bosonic entanglement swapping Bell-state measurement. This is implemented via a bosonic controlled-Z gate and two separate X-basis projective homodyne measurements on the stationary stored codewords. Our approach circumvents mode-mismatch losses associated with routing and interfering of heralding modes on a beamsplitter, and confines losses to those arising from stationary storage. We evaluate the performance of the proposed quantum repeater by calculating its secret key rate under realistic lab environments. Moreover, we explicitly demonstrate that at stationary damping rate of κdamp−1=~\SI{40}{\milli\second}, GBMQR can achieve entanglement generation and swapping success probabilities approx.~0.75, and 0.58 respectively, surpassing the hallmark success probability of 1/2 set by ideal linear beamsplitter-based Bell-state measurements. The proposed device can be implemented using currently available superconducting microwave technology and is suited for secure chip-to-chip communication and distributed quantum computing.
Quantum repeaters constitute a promising platform for enabling long-distance quantum communication and may ultimately serve as the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. An efficient approach to encoding qubits within an error correcting code is provided by bosonic codes, in which even a single oscillator mode can function as a sufficiently large physical system. In this work, we initially investigate the bosonic Gottesman Kitaev Preskill (GKP) code as a promising platform for loss correcting quantum repeaters, compatible with room temperature implementation, and analyse how loss and other noise sources propagate through the circuit using Heisenberg evolution. We analyse three quantum repeater protocols in which transmission loss is suppressed at the cost of logical errors, identifying a relay-like teleamplifier as the optimal scheme. This enables long distance quantum communication via densely packed nodes without higher-level encoding, and we evaluate the resulting secure key rates exploiting analog syndrome information. Furthermore, we propose a concatenated Bell-state measurement (CBSM) scheme with a modified parity encoding based on GKP qubits, CV measurement with teleamplifier and a clipping method that corrects transmission loss without introducing logical errors. This significantly enhances the possible secure key distance. We find that GKP based repeaters can achieve performance comparable to approaches relying on photonic qubits, while requiring orders of magnitude fewer qubits. Our parity encoded GKP repeater protocol achieves a substantially higher secret key rate than existing GKP based repeater schemes while maintaining a comparable resource overhead.
Abstract A quantum repeater scheme based on cavity‐quantum electrodynamics (QED) and quantum error correction of channel loss via rotation‐symmetric bosonic codes (RSBCs) is proposed to distribute atomic entangled states over long distances without memories and at high clock rates. In this scheme, controlled rotation gates, i.e., phase shifts of the propagating light modes conditioned upon the state of an atom placed in a cavity, provide a mechanism both for the entangled‐state preparations and for the error syndrome identifications. In order to assess the performance of this repeater protocol, an explicit instance of RSBCs—multicomponent cat codes—are studied quantitatively. It is found that the total fidelity and the success probability for quantum communication over a long distance (such as 1000 km) both can almost approach unity provided a small enough elementary distance between stations (smaller than 0.1 or 0.01 km) and rather low local losses (up to 0.1%) are considered. In a quantum key distribution application, secret key rates can become correspondingly high, both per channel use, beating the repeaterless bound, and per second thanks to the relatively high clock rates of the memoryless scheme. Based upon the cavity‐QED setting, this scheme can be realized at room temperature and at optical frequencies.
Abstract: This chapter explores the engineering of quantum repeaters, a critical technology for enabling secure and scalable long-distance quantum communication. Quantum repeaters extend the range of quantum communication networks by preserving entanglement and mitigating signal loss over large distances. The chapter covers the key principles of entanglement swapping, quantum memory, and quantum error correction, which are essential for maintaining the integrity of quantum states. It also examines advanced repeater architectures, including multi-mode repeaters and entanglement purification techniques, to improve scalability and robustness. Case studies highlight real-world implementations of quantum repeaters in quantum key distribution (QKD) networks, demonstrating their role in achieving secure global communication. Keywords: quantum repeaters, long-distance quantum communication, entanglement swapping, quantum memory, quantum error correction, entanglement purification, multi-mode repeaters, quantum key distribution, QKD, scalable quantum networks, secure communication.
Abstract Quantum error correction codes based on continuous variables play an important role for the implementation of quantum communication systems. A natural application of such codes occurs within quantum repeater systems which are used to combat severe channel losses and local gate errors. In particular, channel loss drastically reduces the distance of communication between remote users. Here, a cavity‐quantum electrodynamics (QED) based repeater scheme is considered to address the losses in the quantum channel. This repeater scheme relies on the transmission of a specific class of rotationally invariant error‐correcting codes. Several rotation‐symmetric bosonic codes (RSBCs) are compared for encoding the initial states of two remote users connected by a quantum repeater network against the convention of the cat codes and the performance of the system is quantified by using the secret key rate. In particular, the number of stations required to exchange a secret key over a fixed distance is determined and establish the resource overhead. For higher‐loss codes, the results show that a secret key rate (SKR) value of 0.01 bit per channel use can be achieved at a distance of 10000 km, with an elementary distance of 1.3 km.
This thesis is an exploration of quantum repeaters from a practical point of view. Quantum repeaters are devices which help improve the quantum communication capacity of a lossy bosonic channel (which include photonic channels such as optical fiber) beyond what is possible using a purely lossy channel. The analyses in this thesis involve modeling the experimental imperfections inherent in the various devices which comprise a quantum repeater, then combining these models to calculate various quantities of interest. \n \nTwo systems are analyzed in this thesis. One is a simple quantum repeater, while the other is a potential building block for more complex quantum repeaters. \n \nThe simple quantum repeater scheme can be implemented with currently available technology. In it, two parties perform quantum key distribution (QKD) by exchanging photons with two quantum memories placed between them. Its secret key rate ideally scales as the square root of the transmittivity of the optical channel, which is superior to QKD schemes based on direct transmission because key rates for the latter scale at best linearly with transmittivity. Taking into account imperfections in the setup, such as detector efficiency and dark counts, we present parameter regimes in which our protocol outperforms protocols based on direct transmission. We find that implementing our scheme with trapped ions is a promising way to reach the necessary parameter regimes, and that the regimes are easier to reach if the optical channels are very lossy. \n \nThe creation of entanglement between two quantum memories is an important building block in some quantum repeater schemes. We consider a specific quantum memory consisting of an atom trapped in a cavity. The system allows a CNOT operation to be performed between an atom and a photon. We study three methods for taking advantage of this to entangle two atoms: (1) interacting a coherent pulse with each atom, then performing an entangling measurement on the pulses; (2) interacting a single coherent pulse with each atom sequentially; (3) emitting an entangled photon from one atom and interacting it with the other atom. The success probability of each method is compared, as well as the quality of the entangled states produced by each one, taking into account imperfections which appear in a specific experimental implementation of such memories. We find that there is a tradeoff between success probability and entangled state quality when coherent states are used, and that method 3 provides higher-quality entangled states than is possible with the other two methods.