Photonic Greenberger-Horne-Zeilinger (GHZ) states serve as the central resource for a number of important applications in quantum information science, including secret sharing, sensing, and fusion-based quantum computing. The use of photon-emitter entangling gates is a promising approach to creating these states that sidesteps many of the difficulties associated with intrinsically probabilistic methods based on linear optics. However, the efficient creation of high-fidelity GHZ states of many photons remains an outstanding challenge due to both coherent and incoherent errors during the generation process. Here, we propose an entanglement concentration protocol that is capable of generating perfect GHZ states using only local gates and measurements on imperfect weighted graph states. We show that our protocol is both efficient and robust to incoherent noise errors.
Photonic Greenberger-Horne-Zeilinger (GHZ) states serve as the central resource for a number of important applications in quantum information science, including secret sharing, sensing, and fusion-based quantum computing. The use of photon-emitter entangling gates is a promising approach to creating these states that sidesteps many of the difficulties associated with intrinsically probabilistic methods based on linear optics. However, the efficient creation of high-fidelity GHZ states of many photons remains an outstanding challenge due to both coherent and incoherent errors during the generation process. Here, we propose an entanglement concentration protocol that is capable of generating perfect GHZ states using only local gates and measurements on imperfect weighted graph states. We show that our protocol is both efficient and robust to incoherent noise errors.
Probabilistic entangling measurements are key operations in linear-optical quantum technologies, enabling the generation and manipulation of high-dimensional quantum states. While prior research has focused predominantly on specific entangled states, notably graph states and Greenberger-Horne-Zeilinger (GHZ) states, broader classes of states with variable entanglement remain underexplored. In this work, we present a linear-optical approach for generating and fusing GHZ-like states, which generalize standard GHZ states to include variable entanglement degrees. We introduce two schemes based on modified fusion gates that allow flexible control over generation efficiency and the entanglement of the output states. These results offer a promising pathway toward resource-efficient entangled-state generation for scalable quantum computing and communication.
The distribution of high-quality Greenberger-Horne-Zeilinger (GHZ) states is at the heart of many quantum communication tasks, ranging from extending the baseline of telescopes to secret sharing. They also play an important role in error-correction architectures for distributed quantum computation, where Bell pairs can be leveraged to create an entangled network of quantum computers. We investigate the creation and distillation of GHZ states out of nonperfect Bell pairs over quantum networks. In particular, we introduce a heuristic dynamic programming algorithm to optimize over a large class of protocols that create and purify GHZ states. All protocols considered use a common framework based on measurements of nonlocal stabilizer operators of the target state (i.e., the GHZ state), where each nonlocal measurement consumes another (nonperfect) entangled state as a resource. The new protocols outperform previous proposals for scenarios without decoherence and local gate noise. Furthermore, the algorithms can be applied for finding protocols for any number of parties and any number of entangled pairs involved.
Abstract The central technological appeal of quantum science resides in exploiting quantum effects, such as entanglement, for a variety of applications, including computing, communication and sensing 1 . The overarching challenge in these fields is to address, control and protect systems of many qubits against decoherence 2 . Against this backdrop, optical photons, naturally robust and easy to manipulate, represent ideal qubit carriers. However, the most successful technique so far for creating photonic entanglement 3 is inherently probabilistic and, therefore, subject to severe scalability limitations. Here we report the implementation of a deterministic protocol 4–6 for the creation of photonic entanglement with a single memory atom in a cavity 7 . We interleave controlled single-photon emissions with tailored atomic qubit rotations to efficiently grow Greenberger–Horne–Zeilinger (GHZ) states 8 of up to 14 photons and linear cluster states 9 of up to 12 photons with a fidelity lower bounded by 76(6)% and 56(4)%, respectively. Thanks to a source-to-detection efficiency of 43.18(7)% per photon, we measure these large states about once every minute, which is orders of magnitude faster than in any previous experiment 3,10–13 . In the future, this rate could be increased even further, the scheme could be extended to two atoms in a cavity 14,15 or several sources could be quantum mechanically coupled 16 , to generate higher-dimensional cluster states 17 . Overcoming the limitations encountered by probabilistic schemes for photonic entanglement generation, our results may offer a way towards scalable measurement-based quantum computation 18,19 and communication 20,21 .
We present efficient protocols for creating multipartite Greenberger-Horne-Zeilinger (GHZ) and W states of distant stationary qubits. The system nonuniformity and/or the non-ideal single-photon scattering usually limit the performance of entanglement creation, and result in the decrease of the fidelity and the efficiency in practical quantum information processing. By using linear optical elements, errors caused by the system nonuniformity and non-ideal photon scattering can be converted into heralded loss in our protocols. Thus, the fidelity of generated multipartite entangled states keeps unchanged and only the efficiency decreases. The GHZ state of distant stationary qubits is created in a parallel way that its generation efficiency considerably increases. In the protocol for creating the W state of N distant stationary qubits, an input single photon is prepared in a superposition state and sent into N paths parallelly. We use the two-spatial-mode interferences to eliminate the "which path" single-photon scattering "knowledge". As a result, the efficiency of creating the N-qubit W state is independent of the number of stationary qubits rather than exponentially decreases.
Abstract Multipartite entangled states, such as Greenberger–Horne–Zeilinger (GHZ) states, are important resources in multiparty quantum networking tasks. We consider protocols for generating such states from networks of Bell pairs and local operations and classical communication. We present a computationally-efficient protocol for generating GHZ states that is also efficient with respect to the number of consumed Bell pairs, (local) gates, and Bell-pair sources. Our protocol: (1) requires O ( N ) gates in a network with N nodes, independent of the network topology; (2) has time complexity O ( N 2 ), avoiding the Steiner tree and any other computationally-hard problem; (3) maintains a near-optimal number of consumed Bell pairs. Numerically, our protocol outperforms those based on (approximate) Steiner trees with respect to the number of gates and Bell-pair sources. We prove that the minimal Bell-pair source cost is given by solving the graph-theoretic dominating set problem, and we demonstrate numerically that our protocol is nearly optimal for this quantity. Finally, we analytically characterize the impact of noisy Bell pairs and gates on the fidelity of the distributed GHZ states.
Abstract One of the key aims of quantum networks is the efficient distribution of multipartite entangled states among end users. While various architectures have been proposed, each comes with distinct advantages and limitations. Many designs depend on long-lived quantum memories and deterministic gates, which, while powerful, introduce considerable cost and technical challenges. Experimentally cheaper alternatives that circumvent these constraints are often limited to specific types of entanglement and a specific number of users. Here, we present an experiment-friendly quantum server that relies only on linear optical elements, offering a flexible approach to multipartite entanglement distribution. Our so-called photon-weaving quantum server can generate and distribute one of several locally nonequivalent graph states, including Greenberger–Horne–Zeilinger (GHZ) states, as well as path, cycle, and caterpillar graph states. This is achieved through two distinct fusion protocols, i.e. multiphoton graph-state fusion ( graph-state weaving ) and multiphoton GHZ-state fusion ( GHZ-state weaving ), and can readily be implemented.