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.
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.
Generating large multiphoton entangled states is of main interest due to enabling universal photonic quantum computing and all-optical quantum repeater nodes. These applications exploit measurement-based quantum computation using cluster states. Remarkably, it was shown that photonic cluster states of arbitrary size can be generated by using feasible heralded linear optics fusion gates that act on heralded three-photon Greenberger-Horne-Zeilinger (GHZ) states as the initial resource state. Thus, the capability of generating heralded GHZ states is of great importance for scaling up photonic quantum computing. Here, we experimentally demonstrate this required building block by reporting a polarisation-encoded heralded GHZ state of three photons, for which we build a high-rate six-photon source (547±2 Hz) from a solid-state quantum emitter and a stable polarization-based interferometer. The detection of three ancillary photons heralds the generation of three-photon GHZ states among the remaining particles with fidelities up to F=0.7278±0.0106. Our results initiate a path for scalable entangling operations using heralded linear-optics implementations.
Probabilistic and destructive Bell-measurements, also known as fusions, constitute a fundamental primitive for photonic quantum technologies. These operations rely only on pairwise photonic interference, whereas the computational power of photonic quantum systems originates from many-body interference. Here, we introduce a family of high-efficiency linear-optical GHZ measurements based on four-mode interferometers and show that incorporating many-body interference into this ubiquitous primitive leads to more efficient entangling operations. For the four-photon case, the success probability is 9/32, and adaptive variants ensure that unsuccessful events project onto useful stabilizer states. We further show that the approach naturally generalizes to larger GHZ measurements, yielding an exponentially higher success probability than previous linear-optical schemes. Finally, we demonstrate practical advantages for graph-state resource generation, entanglement distribution between remote spin-photon interfaces, and fusion-based quantum computing. Our results establish high-efficiency many-body measurements as a new primitive for scalable photonic quantum information processing.
High-dimensional multipartite entanglement plays a crucial role in quantum information science. However, existing schemes for generating such entanglement become complex and costly as the dimension of quantum units increases. In this Letter, we overcome the limitation by proposing a significantly enhanced linear optical heralded scheme that generates the d-level N-partite Greenberger-Horne-Zeilinger (GHZ) state with single-photon sources and linear operations. Our scheme requires dN photons, which is the minimal required photon number, with substantially improved success probability from previous schemes. It employs linear optical logic gates compatible with any qudit encoding system and can generate generalized GHZ states with installments of beam splitters. With efficient generations of high-dimensional resource states, our work opens avenues for further exploration in high-dimensional quantum information processing.
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 .
Fusion measurements are a key primitive for linear-optical quantum computing and quantum networks. Type-I and type-II fusion gates are widely used to combine small entangled resource states into larger photonic states, but without ancillary resources their success probability is limited to 1/2. Existing 3/4-efficient type-I schemes rely on entangled Bell-pair ancillary states, whose preparation is itself probabilistic and resource-intensive. Here we propose a boosted type-I fusion gate using only four ancillary single photons and standard linear-optical primitives. For multiqubit GHZ and graph states, the gate succeeds directly with probability 5/8, while a distillation protocol converts partially entangled outcomes into additional successful events, raising the total success probability to 11/16 after one stage and asymptotically to 3/4. We quantify the practical advantage of this scheme by estimating the photonic resources required for generating representative large entangled photonic states and show that the proposed gate significantly reduces the required overhead compared with existing schemes. These results expand the set of resource-efficient linear-optical primitives and enable a substantial reduction in the resource requirements for scalable photonic quantum computing and quantum communication.
Abstract One of the most important resources for quantum optical experiments and applications are on-demand highly entangled multiphoton quantum states. A promising way of generating them is heralding entanglement generation at a high rate from letting independent photons interfere. However, such schemes often work for a specific internal degree of freedom of the interfering photons only. Going to higher numbers of entangled photons, the success probabilities decrease while the number of necessary resources, e.g. auxiliary photons and optical elements, increases. To make probabilistic schemes feasible also for larger quantum states, it is therefore important to find resource-efficient generation schemes with high success probabilities. In this work, we introduce easily implementable schemes to herald qubit Greenberger–Horne–Zeilinger (GHZ) states, higher-dimensional Bell states and higher-dimensional three-party GHZ states. Our schemes solely rely on multiphoton interference, i.e. they can be adjusted to work for arbitrary degrees of freedom. Furthermore, they demonstrate high success probabilities and need comparably few auxiliary photons.