Graph states are an important class of multipartite entangled states. Previous experimental generation of graph states and in particular the Greenberger-Horne-Zeilinger (GHZ) states in linear optics quantum information schemes is subjected to an exponential decay in efficiency versus the system size, which limits its large-scale applications in quantum networks. Here, we demonstrate an efficient scheme to prepare graph states with only a polynomial overhead using long-lived atomic quantum memories. We generate atom-photon entangled states in two atomic ensembles asynchronously, retrieve the stored atomic excitations only when both sides succeed, and further project them into a four-photon GHZ state. We measure the fidelity of this GHZ state and further demonstrate its applications in the violation of Bell-type inequalities and in quantum cryptography. Our work demonstrates the prospect of efficient generation of multipartite entangled states in large-scale distributed systems with applications in quantum information processing and metrology.
Graph states are an important class of multipartite entangled states. Previous experimental generation of graph states and in particular the Greenberger-Horne-Zeilinger (GHZ) states in linear optics quantum information schemes is subjected to an exponential decay in efficiency versus the system size, which limits its large-scale applications in quantum networks. Here, we demonstrate an efficient scheme to prepare graph states with only a polynomial overhead using long-lived atomic quantum memories. We generate atom-photon entangled states in two atomic ensembles asynchronously, retrieve the stored atomic excitations only when both sides succeed, and further project them into a four-photon GHZ state. We measure the fidelity of this GHZ state and further demonstrate its applications in the violation of Bell-type inequalities and in quantum cryptography. Our work demonstrates the prospect of efficient generation of multipartite entangled states in large-scale distributed systems with applications in quantum information processing and metrology.
Distributed entanglement across multi-node quantum networks is essential for a wide range of quantum technologies, including modular quantum computers, distributed sensing and metrology, and multi-party secure communication protocols. Such large-scale quantum networks will require photonic interconnects to generate and sustain entangled states across localized nodes. Previously, three-node distributed Greenberger-Horne-Zeilinger (GHZ) states have been generated between solid-state qubits and atomic ensembles, but not yet in the platform of individual atomic qubits, which can be replicated, detected, and individually controlled with high fidelity. Here we report the first fully-distributed GHZ state of qubits across a three-node quantum network of single atomic memories, using photonic interconnects. We achieve a bounded fidelity of 0.841(17)≤F≤0.881(17) at an entanglement generation rate of 0.095(5)/sec and measure a clear violation of Mermin's inequality while closing the detection loophole for the first time in a fully-distributed multipartite entangled state.
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.
We consider the quantum memory assisted quantum state verification task, where an adversary prepares independent multipartite entangled states and sends them to the local verifiers, who then store several copies in the quantum memory and measure them collectively to make a decision. We establish an exact analytic formula for optimizing two-copy state verification, where the verifiers store two copies, and give a globally optimal two-copy strategy for multiqubit graph states involving only Bell measurements. When the verifiers can store arbitrarily many copies, we present a dimension expansion technique that designs efficient verification strategies for this case, showcasing its application to efficiently verifying Greenberger-Horne-Zeilinger (GHZ)-like states. These strategies become increasingly advantageous with growing memory resources, ultimately approaching the theoretical limit of efficiency. Our findings demonstrate that quantum memories enhance state verification efficiency, shedding light on error-resistant strategies and practical applications of large-scale quantum memory assisted verification.
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 .
Graph states-one of the most representative families of multipartite entangled states-are important resources for multiparty quantum communication, quantum error correction, and quantum computation. Device-independent certification of highly entangled graph states plays a prominent role in quantum information processing tasks. Here we have experimentally demonstrated device-independent certification for multipartite graph states by adopting the robust self-testing scheme based on scalable Bell inequalities. Specifically, the prepared multi-qubit Greenberger-Horne-Zeilinger (GHZ) states and linear cluster states achieve a high degree of Bell violation, which are beyond the nontrivial bounds of the robust self-testing scheme. Furthermore, our work paves the way to the device-independent certification of complex multipartite quantum states.
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.