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arXiv:2604.14516 · Physical Review A

Linear Optical Schemes to Postselect High-Dimensional Dicke States

Daniel Bhatti, William J. Munro, Seungbeom Chin

quant-phSubmitted Apr 16, 2026• Announced Apr 17, 2026• 0 citations
arXivHTMLPDF

Abstract

Multipartite entanglement is an essential quantum resource for various distributed quantum applications. One promising method for preparing multipartite entanglement is to interfere independent photons at linear optical interference setups. While heralding the successful interference and thereby the state generation is often costly, postselecting entangled states provides an achievable alternative in this framework. We introduce a family of interference schemes for postselecting symmetric qudit Dicke states, useful resources in quantum communication and variational quantum computing. We present schemes with and without ancillary photons and show that using ancillary photons can exceed the upper bound on the success probability of schemes without ancillary photons. Our results accommodate a wide range of linear optical schemes, providing multiple viable approaches for postselecting Dicke states.

Journal reference
Phys. Rev. A 114, 013714 (2026)
DOI
10.1103/xlzr-7qvz

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Multipartite entanglement is an essential quantum resource for various distributed quantum applications. One promising method for preparing multipartite entanglement is to interfere independent photons at linear optical interference setups. While heralding the successful interference and thereby the state generation is often costly, postselecting entangled states provides an achievable alternative in this framework. We introduce a family of interference schemes for postselecting symmetric qudit Dicke states, useful resources in quantum communication and variational quantum computing. We present schemes with and without ancillary photons and show that using ancillary photons can exceed the upper bound on the success probability of schemes without ancillary photons. Our results accommodate a wide range of linear optical schemes, providing multiple viable approaches for postselecting Dicke states.
Entangled states of photons form the backbone of many quantum technologies. Due to the lack of effective photon-photon interactions, the generation of these states is typically probabilistic. In the prevailing but fundamentally limited generation technique, known as postselection, the target photons are measured destructively in the generation process. By contrast, in the alternative approach-heralded state generation-the successful creation of a desired state is verified by the detection of ancillary photons. Heralded state generation is superior to postselection in several critical ways: it enables free usage of the prepared states, allows for the success probability to be arbitrarily increased via multiplexing, and provides a scalable route to quantum information processing using photons. Here, we review theoretical proposals and experimental realisations of heralded entangled photonic state generation, as well as the impact of realistic experimental errors. We then discuss the wide-ranging applications of these states for quantum technologies, including resource states in linear optical quantum computing, entanglement swapping for repeater networks, fundamental physics, and quantum metrology.
Entanglement is a fundamental feature of quantum mechanics and a key resource for quantum information processing. Among multipartite entangled states, Dicke states ∣Dnk⟩|D_n^k\rangle∣Dnk​⟩ are distinguished by their permutation symmetry, which provides robustness against particle loss and enables applications for quantum communication and computation. Although Dicke states have been realized in various platforms, most optical implementations rely on postselection, which destroys the state upon detection and prevents its further use. A heralded optical scheme is therefore highly desirable. Here, we present a linear-optical heralded scheme for generating arbitrary Dicke states ∣Dnk⟩|D_n^k\rangle∣Dnk​⟩ with 3n+k3n+k3n+k photons through the framework of the linear quantum graph (LQG) picture. By mapping the scheme design into the graph-finding problem, and exploiting the permutation symmetry of Dicke states, we overcome the structural complexity that has hindered previous approaches. Our results provide a resource-efficient pathway toward practical heralded preparation of Dicke states for quantum technologies.
In this paper, we propose a linear-optical quantum computation scheme that starts from high-dimensionally entangled qudits but performs quantum computation on qubits defined in their subspaces. This approach enables us to increase the success probability of linear-optical fusions from 50%50\%50% to 1−1/d1-1/d1−1/d for qudits of dimension ddd without relying on existing approaches using ancilla photons and quantum codes. In particular, we show that a 2D cluster state of qubits can be generated from 5-qudit 1D cluster states using pairwise fusion gates while preserving their boosted success probability. We numerically demonstrate that this approach can improve the loss tolerance of a percolation-based scheme while keeping the photon number per resource state constant.
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.
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 1/21/21/2. Existing 3/43/43/4-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 5/85/85/8, while a distillation protocol converts partially entangled outcomes into additional successful events, raising the total success probability to 11/1611/1611/16 after one stage and asymptotically to 3/43/43/4. 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.