Linear Optical Schemes to Postselect High-Dimensional Dicke States
Daniel Bhatti, William J. Munro, Seungbeom Chin
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.
AI Impact Assessments
(3 models)Scientific Impact Assessment
Core Contribution
This paper addresses the problem of generating high-dimensional (qudit) symmetric Dicke states using linear optical setups with postselection. The main novelty lies in presenting a systematic family of interference schemes that work for arbitrary qudit dimension *d* and arbitrary particle number *N*, covering both ancilla-free and ancilla-assisted protocols. The key result is demonstrating that ancilla-assisted schemes can exceed the theoretical upper bound on success probability achievable by ancilla-free schemes. Specifically, the authors derive closed-form success probabilities for all proposed schemes and identify the crossover regimes (via linear fits) where ancillary photons become beneficial.
The paper extends prior work on qubit Dicke state postselection (e.g., Refs. [23–25, 29]) to the high-dimensional setting, filling a gap in the literature where qudit generalizations were lacking. The ancilla-assisted scheme generalizes the W-state protocol of Kim et al. [29] to arbitrary Dicke states in arbitrary dimensions.
Methodological Rigor
The approach is methodologically sound, employing a clean formalism based on second-quantization operators and discrete Fourier transform unitaries. The progression from operator-level descriptions to concrete linear optical implementations is well-structured and pedagogically clear. The derivations of success probabilities (Eqs. 10, 14, 15, 25, 27, 28) follow logically, and the optimization over beam splitter transmissivity (Eq. 26) is straightforward but important.
However, there are notable limitations in rigor:
1. No noise analysis: The paper acknowledges this but does not incorporate photon loss, detector imperfections, or source impurities, which are critical for practical relevance. The brief mention that success probabilities remain above dark-count rates (Fig. 4 caption) is helpful but insufficient for a realistic assessment.
2. No fidelity analysis: The paper assumes perfect operations throughout. No discussion of how mode mismatch, partial distinguishability, or realistic beam splitter imperfections would affect the fidelity of the postselected states.
3. Limited numerical verification: The analytical results are not cross-validated with numerical simulations of the optical circuits, which would strengthen confidence, especially for larger systems.
4. The comparison framework is somewhat asymmetric: The ancilla-free "upper bound" (Eq. 10) assumes access to multiphoton Fock states, while the ancilla-assisted scheme is evaluated with single-photon inputs. While the authors acknowledge this, the comparison could be more carefully framed.
Potential Impact
Quantum Communication & Networks: Dicke states are known resources for quantum secret sharing, anonymous communication, and quantum repeater protocols. Providing practical generation schemes in higher dimensions could enable more efficient protocols that exploit the denser encoding of qudits.
Variational Quantum Computing: The mention of Dicke states in variational quantum computing (Ref. [20]) adds relevance, though the connection is not deeply explored in the paper.
Experimental Photonics: The schemes are designed with current photonic technology in mind—symmetric multiport splitters, beam splitters, and single-photon sources. The alternative qubit scheme in Appendix A using only BSs and PBSs is particularly practical. However, the scalability to large *N* faces the same fundamental challenges as other postselection-based approaches: exponentially decreasing success probabilities.
Theoretical Framework: The operator-level approach and the connection to linear quantum graphs (Ref. [30]) provide a useful theoretical lens that could inspire further work on other entangled state families (phased Dicke states, anti-symmetric states, as the authors suggest).
The practical impact is moderate. Postselection probabilities decrease rapidly with *N*, making large-scale generation impractical without further innovations (e.g., multiplexing, heralding). The paper itself acknowledges that extending to heralding is a crucial next step.
Timeliness & Relevance
The work is timely in several respects:
However, the field is moving toward heralded (not postselected) schemes, as postselection limits scalability and is incompatible with many networking applications. The paper acknowledges this but does not bridge the gap.
Strengths
1. Generality: The framework covers arbitrary qudit dimension *d*, arbitrary particle numbers *N*, and arbitrary occupation vectors k, providing a comprehensive toolkit.
2. Analytical tractability: Closed-form expressions for all success probabilities enable direct comparison and optimization.
3. Clear demonstration of ancilla advantage: The finding that ancillary photons can beat the ancilla-free upper bound is a clean and useful result with a clear physical interpretation (reducing the output state space via 2×2 splitters).
4. Multiple implementation options: Offering several schemes with different resource-performance tradeoffs gives experimentalists flexibility.
5. Clear presentation: The paper is well-organized with a logical flow from abstract to concrete.
Limitations
1. No noise/loss analysis limits practical applicability.
2. Postselection-only: The approach inherently cannot scale to large systems or be used in protocols requiring deterministic state preparation.
3. Limited novelty in techniques: The mathematical tools (DFT unitaries, symmetric multiport splitters, postselection) are well-established; the contribution is primarily in their systematic application to qudit Dicke states.
4. No experimental validation or concrete experimental proposal with specific hardware parameters.
5. The crossover analysis (Fig. 5), while useful, is based on idealized success probabilities and may shift significantly under realistic conditions.
Overall Assessment
This is a solid, well-executed theoretical contribution that systematically addresses qudit Dicke state postselection in linear optics. It fills a clear gap in the literature and provides useful analytical results. However, the incremental nature of the generalization from qubits to qudits, the absence of noise analysis, and the inherent limitations of postselection-based approaches limit its broader impact.
Generated Apr 17, 2026
Comparison History (38)
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Paper 2 is likely to have higher impact due to clearer near-term experimental applicability and broader utility: it proposes concrete linear-optical architectures to generate high-dimensional multipartite entanglement (symmetric qudit Dicke states), relevant to quantum communication and variational/photonic quantum computing. The work offers design families, compares ancilla-assisted vs ancilla-free success probabilities, and provides actionable schemes that experimental groups can implement and benchmark. Paper 1 is conceptually novel in identifying contextuality in QND/state-discrimination settings (including noise), but its impact is more foundational and may be narrower in immediate technological uptake.
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Paper 2 addresses a practical and broadly applicable problem—generating multipartite entangled Dicke states using linear optics—with direct relevance to quantum communication and variational quantum computing. It introduces novel interference schemes with and without ancillary photons and proves that ancillary photons can surpass fundamental bounds, offering both theoretical insight and experimental pathways. Paper 1 analyzes coherence dynamics within the HHL algorithm, which is more niche and primarily analytical without clear new algorithmic or experimental implications. Paper 2's broader applicability and experimental relevance give it higher impact potential.
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Paper 2 addresses the fundamental problem of generating multipartite entangled states (high-dimensional Dicke states) using linear optics, which has broad applications across quantum communication, quantum computing, and quantum information science. It introduces a general family of schemes with rigorous analysis of success probabilities and proves that ancillary photons can exceed fundamental bounds. Paper 1 proposes a specialized detection scheme for quantum LiDAR with narrower applicability. Paper 2's broader relevance to multiple quantum technology fields, methodological generality, and foundational nature give it higher potential impact.
Paper 1 likely has higher impact: it delivers a strong, general no-go style bound (logarithmic ceiling on encoding rate) for an emerging code class, extends to subsystem codes and added unitaries, and derives results from a broader automorphism-group theorem with potential reuse across quantum coding theory. The explicit k=4 counterexample with a transversal non-Clifford gate is also notable. Paper 2 proposes useful linear-optical postselection schemes, but appears more incremental and application-specific, with impact depending on experimental feasibility and success probabilities.
Paper 1 addresses the critical challenge of operating in noisy environments, which is highly relevant for near-term quantum devices. By providing a scalable framework for quantum-enhanced metrology under realistic noise conditions, it offers more immediate and practical real-world applications. In contrast, Paper 2 relies on postselection techniques, which traditionally face significant scalability limitations in generating multipartite entanglement.
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