Constant Overhead Entanglement Distillation via Scrambling.

Quantum networks aim to facilitate the fault-tolerant and secure transmission of quantum states across distant devices. The widely adopted quantum teleportation scheme requires multiple rounds of entanglement swapping and purification, leading to significant resource overhead and operational complexity. In this study, we propose a novel fault-tolerant and secure quantum communication scheme based on uncorrectable error injection. Our method exploits a quantum state encoding scheme based on quantum error correction codes, which strategically introduces uncorrectable errors to enhance security. It eliminates the need for entanglement distribution while reducing resource requirements. The injected errors protect against eavesdropping by preventing unauthorized parties from retrieving meaningful information. Security analysis shows that as the data length and encoded message size increase, information leakage becomes negligible relative to the size of the total message. Comparative performance analysis with existing approaches indicates that our method reduces transmission overhead while maintaining comparable fidelity in low-error regimes. These findings suggest that the proposed method offers a scalable and practical alternative for secure long-distance quantum communication, distributed quantum computing, and future quantum internet applications.

Distributed quantum computing relies on coordinated operations between remote quantum processing units (QPUs), yet most existing work either assumes full connectivity, unrealistic for large networks, or relies on entanglement swapping. To mitigate the overhead of communication, we propose a scheme for the distribution of collective quantum operations among remote quantum processing units by exploiting distributed fan-out operations to a central node in network architectures similar to those used for high-performance computing, which requires only pre-shared entanglement, local operations and classical communication. We show that a general diagonal gate can be distributed among any number of nodes and provide the ebit cost bounds. For a single distributed multicontrolled gate, this amounts to a single additional Bell pair over the theoretically optimal calculation with all-to-all pre-shared entanglement, demonstrating better scalability when compared to current proposals based on entanglement swapping through a network. We provide a recipe for the lumped distribution of gates such as arbitrarily-sized Toffoli and multicontrolled Z, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{zz}(\theta)$</tex-math></inline-formula> gates. Finally, we provide an exact implementation of a distributed Grover's search algorithm using this protocol to partition the circuit, with Bell pair cost growing linearly with the number of Grover iterations and the number of partitions, and show how these techniques can be applied to other algorithms such as QAOA. Our results show that alternative approaches to entanglement swapping can provide major benefits in distributed quantum computing, pointing to promising avenues for future research.

Individual atoms in optical cavities can provide an efficient interface between stationary qubits and flying qubits (photons), which is an essentiel building block for quantum communication. Furthermore, cavity assisted controlled-not (CNOT) gates can be used for swapping entanglement to long distances in a quantum repeater setup. Nonetheless, dissipation introduced by the cavity during the CNOT may increase the experimental difficulty in obtaining long-distance entanglement distribution using these systems. We analyse and compare a number of cavity-based repeater schemes combining various entanglement generation schemes and cavity assisted CNOT gates. We find that a scheme, where high-fidelity entanglement is first generated in a two-photon detection scheme and then swapped to long distances using a recently proposed heralded CZ-gate exhibits superior performance compared to the other schemes. The heralded gate moves the effect of dissipation from the fidelity to the success probability of the gate thereby enabling high-fidelity entanglement swapping. As a result, high-rate entanglement distribution can be achieved over long distances even for low cooperativities of the atom-cavity systems. This high-fidelity repeater is shown to outperform the other cavity-based schemes by up to two orders of magnitude in the rate for realistic parameters and large distances (1000 km).

Distillation of entanglement using only Gaussian operations is an important primitive in quantum communication, quantum repeater architectures, and distributed quantum computing. Existing distillation protocols for continuous degrees of freedom are only known to converge to a Gaussian state when measurements yield precisely the vacuum outcome. In sharp contrast, non-Gaussian states can be deterministically converted into Gaussian states while preserving their second moments, albeit by usually reducing their degree of entanglement. In this work-based on a novel instance of a noncommutative central limit theorem-we introduce a picture general enough to encompass the known protocols leading to Gaussian states, and new classes of protocols including multipartite distillation. This gives the experimental option of balancing the merits of success probability against entanglement produced.

With their ability to process and transfer quantum information, large-scale entanglement-based quantum networks could be at the heart of a new age of quantum information, enabling fundamentally new applications such as distributed quantum computation, quantum communication, and quantum enhanced sensing. Due to their long spin coherence, controllable local qubit registers and optically active spins, color centers in diamond are prime candidates for nodes of such a network, and have enabled some of the most advanced quantum network demonstrations to date. These demonstrations include the distribution of a 3-node GHZ state across a quantum network, entanglement swapping, entanglement distillation, and memory-enhanced quantum communication. To move beyond current proof-of-principle networks, a further increase of entanglement generation rates is crucial. This thesis presents theoretical and experimental work on enhancing the spin-photon interface of color centers in diamond to achieve this goal, making use of the Purcell effect. The discussed work follows two main directions: embedding of color centers in open, tuneable Fabry-Perot micro-cavities, and in all-diamond photonic crystal cavities. First, we describe theoretical and experimental progress towards cavity-enhanced quantum networks based on nitrogen-vacancy (NV) centers in diamond. Due to their first order sensitivity to electric fields, we choose to embed NV centers in microns-thin diamond membranes that can be integrated into open fiber-based micro-cavities. We develop analytical methods to optimize the design of such open cavity systems for maximum Purcell enhancement of embedded color centers. We demonstrate a method to fabricate optically coherent NV centers in microns-thin diamond membranes, and use such structures to demonstrate the resonant excitation and detection of coherent, Purcell enhanced NV emission. A theoretical model in excellent agreement with our results suggests our system can improve entanglement rates between distant NV centers by two orders of magnitude with near-term improvements to the setup. Second, we describe progress towards an efficient spin-photon interface of group-IV color centers in diamond by coupling them to photonic nanostructures, allowing for large-scale integration. Due to their first-order insensitivity to electric fields, group-IV color centers can be brought in close proximity to surfaces (~ 100 nm), allowing for sub-wavelength mode volumes and thus very high Purcell factors. We numerically optimize photonic crystal cavity designs to maximize the Purcell enhancement of embedded emitters, test the robustness of our designs to real-world fabrication imperfections, and devise a method to efficiently interface nanophotonic structures. We then proceed to fabricate all-diamond photonic crystal cavities, making use of a dry etching technique that is selective to different crystallographic directions, and characterize the resulting optical quality factors. Finally, we marry the developed fabrication methods to fabricate microns-sized diamond platelets that can be transferred from a holding frame in a controlled fashion. This capability could be crucial for the realization of hybrid photonic circuits that we expect to be at the heart of future large-scale quantum networks.

Having multiple Bell pairs shared by distant quantum registers provides a key resource for both quantum networks and distributed quantum computing. In this paper, we present a protocol for parallelized Bell-pair generation that uses the phase of a coherent light pulse to encode a qudit, enabling the simultaneous generation of multiple Bell pairs. By encoding a qudit in a basis of light-matter Schr\"odinger's cat states, the loss of a photon in transit can be detected through an $XX$ parity syndrome, allowing the backaction due to the lost photon to be deterministically corrected through single-qubit rotations. The protocol presented here is compatible with existing technologies in both optical and microwave (circuit QED) architectures, supporting near-term implementation across diverse quantum platforms.

Quantum networks interconnecting quantum processor nodes via optical fibers promise groundbreaking applications in fields like secure communication, distributed quantum computing, and enhanced quantum sensing [1]. These networks require quantum frequency conversion (QFC) to bridge the spectral gap between the optical fibers' low-absorption window near 1550 nm and the qubit platform-specific emission wavelength in the visible spectrum.

The distribution of maximal entanglement stands as a pivotal technique in long-distance practical quantum communication. Specifically, achieving high-fidelity entanglement distribution leans upon efficacious entanglement purification and entanglement concentration. In this paper, we materialize error-rejecting nonlocal entanglement purification protocol (EPP) and entanglement concentration protocol (ECP) for solid-state emitter systems assisted by the scattering property of photon-emitter in one-dimensional waveguide. The parity-check gates of both the EPP and ECP can herald the faulty events with the help of the detectors that click, so they are accomplished, in principle, with unity fidelities, which are conducive to implement two protocols. Moreover, additional emitters are unnecessary except a single photon.

Entanglement generation over large distances is a challenging task due to photon loss, which grows exponentially with link length (e.g., optical fiber). Moreover, EPR pair generation over noisy channels results in imperfect states. Thus, a link is associated with a success probability and an initial fidelity for successfully-generated entanglement. Over time, fidelity de-creases due to environmental noise. Entanglement purification is a way of probabilistically increasing state fidelity. Traditionally, purification protocols perform the following steps: generate two or more EPR pairs between two nodes, execute a series of quantum gates on both sides, and exchange results via classical messages. In this work, we propose a twist on the original entanglement pumping scheme, wherein a fixed number of purification steps are performed successively, before the classical information exchange. This modification introduces optimism to the overall procedure, such that classical communication is performed only at the end, to check the measurement results. The protocol is also optimistic about entanglement generation and does not wait for heralding signals before attempting purification. We study the effect of being optimistic on fidelity and the waiting time to generate an entangled pair as a function of the distance between network nodes. We observe an improvement in both fidelity and expected waiting time. We also study the effect of the number of purification steps on fidelity and latency and observe that typically no more than two or three purification steps are needed when limited by only two memories.

Purpose of the study: systematization and critical analysis of existing approaches to error suppression in quantum repeaters, as well as to assess their advantages and limitations for the implementation of scalable quantum networks and the quantum internet. Methods of research: the paper provides a detailed analysis of modern literature, including a comparison of various quantum repeater schemes, as well as an assessment of resource costs and performance. Result(s): quantum repeaters can be divided into three generations, each of which demonstrates optimal efficiency under certain conditions. The first generation, implementing probabilistic error suppression by generating heralded entanglement and two-way entanglement distillation, is easy to implement and provides the basic functionality of a quantum network, but requires significant time due to the need to exchange classical signals and long-term storage of quantum states. The second generation combines probabilistic entanglement generation with deterministic operation error suppression using quantum error correction, which reduces the requirements for long-term quantum memory, although the exchange of classical signals between neighboring nodes remains mandatory. The third generation relies entirely on deterministic error suppression using one-way classical communication, which allows for a significant reduction in time delays and high entanglement generation rates, despite the need for a denser arrangement of repeaters and high-quality local gates. In addition, the review covers new areas such as memoryless repeaters and all-photonic repeaters. The conducted comparative analysis of resource costs demonstrates that optimization of repeater operating parameters is a key factor for the implementation of scalable quantum networks, which is of direct importance for quantum key distribution, quantum metrology, and distributed quantum computing. Scientific novelty: the scientific novelty lies in the integration of disparate approaches to the implementation of quantum repeaters into a single holistic representation, which allows for an objective assessment of their efficiency by key parameters. The review highlights the potential for new classes of repeaters, such as memoryless repeaters and all-photonic circuits, to become important elements in the development of a quantum internet.

Exploiting the input-output process of low-Q cavities confining nitrogen-vacancy centers, we present an efficient entanglement concentration protocol on electron spin state in decoherence free subspace. Less entangled state can be concentrated to maximally entangled state with the assistance of single photon detection. With its robustness and scalability, the present protocol is immune to dephasing and can be further applied to quantum repeaters and distributed quantum computation.

Recently, a quantum secure direct communication (QSDC) protocol based on the mixture of Bell state particles and single photons[Acta Phys. Sin. 65 230301(2016)] was put forward. In this QSDC protocol, the single photons and the Bell states were both used as information carriers. To be specific, each Bell state as well as single photon was encoded by three bits of classical information. After the sender told the receiver how to measure the particles, the receiver could read out the secret message sent by the sender. Speciously, the information transmission efficiency of this protocol was high. Unfortunately, there exists the information leakage problem in this protocol. When the sender announces that the receiver uses the Z-basis to measure a single photon, everyone knows that the sent secret message is 000 or 001, that is, the first two bits are leaked out; when the sender announces that the receiver uses the X-basis to measure a single photon, everyone knows that the sent secret message is 010 or 011, that is, the first two bits are leaked out too; when the sender announces that the receiver uses the Bell-basis to measure a pair of particles from a Bell state, everyone knows that the sent secret message is 100, 101, 110 or 111, that is, the first bit is leaked out. In a word, two of the three bits of classical information encoded in a single photon, and one of the three bits of classical information encoded in a Bell state are leaked out. Therefore, this scheme is not secure. On the basis of keeping the original idea and changing the contents of the protocol as less as possible, we put forward an improved message encoding rule to solve the information leakage problem, that is, the single photon is only encoded by one bit of classical information, and the Bell state is only encoded by two bits of classical information. In fact, this makes the information capacity of the improved protocol achieves the Helovo bound. So it has high coding capacity. We hope researchers pay more attention to the information leakage problem in quantum secure communication protocols, and thus design truly secure ones.

In distributed quantum computation, small devices composed of a single or a few qubits are networked together to achieve a scalable machine. Typically, there is an optically active matter qubit at each node, so that photons are exploited to achieve remote entanglement. However, in many systems the optically active states are unstable or poorly defined. We report a scheme to perform a high-fidelity entanglement operation even given severe instability. The protocol exploits the existence of optically excited states for phase acquisition without actually exciting those states; it functions with or without cavities and does not require number-resolving detectors.

Precise time synchronization is a fundamental challenge in distributed quantum systems, with direct implications for secure communication, sensing, and next-generation network technologies. In this study, we present a Field Programmable Gate Array (FPGA)-based implementation of a Time-Correlated Entangled Photons (TCEP) source-based synchronization system, achieving <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sub-nanosecond</i> accuracy with timing jitter consistently below 200 ps for a distance up to 20 km. The system leverages the strong temporal correlations inherent in entangled photon pairs to compute synchronization offsets between spatially separated nodes. The design features a modular architecture with optimized kernels for temporal correlation, data aggregation, and normalization, enabling efficient resource utilization and high-throughput performance. Experimental validation demonstrates the FPGA's ability to process photon timestamp data and compute cross-correlation functions significantly faster than traditional CPU-based approaches, achieving execution times in the millisecond range even for large datasets. Our FPGA implementation achieved a consistent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> 800 times speedup over CPU, with performance largely unaffected by channel length. Resource utilization analysis highlights the scalability of the design, with the fully integrated system operating at a clock frequency of 397.5 MHz while maintaining efficient use of logic elements, registers, and memory blocks. This hardware-efficient approach provides the timing backbone for next-generation technologies, facilitating advancements in ultra-reliable low-latency communication, distributed quantum computing, quantum-enhanced sensing, navigation, and lays a foundation for forthcoming 6G networks and the quantum internet.

We introduce and analyze a task that we call Markovianization, in which a tripartite quantum state is transformed to a quantum Markov chain by a randomizing operation on one of the three subsystems. We consider cases where the initial state is a tensor product of n copies of a tripartite state ρABC, and is transformed to a quantum Markov chain conditioned by Bn with a small error, by a random unitary operation on An. In an asymptotic limit of infinite copies and vanishingly small error, we analyze the Markovianizing cost, that is, the minimum cost of randomness per copy required for Markovianization. For tripartite pure states, we derive a single-letter formula for the Markovianizing costs. Counterintuitively, the Markovianizing cost is not a continuous function of states, and can be arbitrarily large even if the state is an approximate quantum Markov chain. Our results have an application for distributed quantum computation.