Quantum Secure Aggregation Overview

• Quantum Secure Aggregation is a family of protocols that uses quantum resources like entanglement and superposition to ensure secure aggregation without exposing individual inputs.
• It leverages mechanisms such as GHZ state distribution, quantum homomorphic encryption, and threshold secret sharing to compute sums and other functions over distributed data.
• The framework guarantees privacy, robustness, and post-quantum security, making it vital for applications in federated learning, sensor networks, and collaborative analytics.

Quantum Secure Aggregation (QSA) encompasses a family of cryptographic protocols leveraging quantum information to realize the privacy-preserving aggregation of data across multiple distributed parties, without exposing individual inputs, and with resilience against both classical and quantum adversaries. QSA frameworks generalize the classical secure aggregation paradigm—ubiquitous in privacy-sensitive federated learning, distributed sensing, and collaborative analytics—by harnessing quantum resources such as entanglement, superposition, and quantum cryptographic primitives. This article presents a detailed examination of QSA methodologies, architectures, security definitions, resource requirements, and deployed applications with explicit reference to primary protocols in the literature.

1. Quantum Aggregation Frameworks and Functional Properties

QSA protocols instantiate aggregation primitives such that a designated aggregator (or the participants collectively) computes the sum, mean, intersection cardinality, or more general functions over private inputs $(x_1, ..., x_n)$ held by $n$ mutually distrustful parties, without leakage of any further individual information. Common functional goals include secure summation $S = \sum_i x_i$ mod $d$, modulo intersection $|\cap_i S_i|$, or federated model parameter updates. Quantum protocols enforce these by combining quantum information processing (entangled states, quantum secret sharing, quantum homomorphic encryption) and classical cryptographic masking.

Principal security properties are formalized as follows:

• Correctness: Aggregator recovers the intended aggregate value under honest execution.
• Privacy: Any coalition of up to $t-1$ participants (for $(t,n)$ threshold schemes), or any adversary (for information-theoretic protocols), learns no additional information about individual inputs.
• Robustness and Verifiability: Errors, deviations, or protocol subversion by parties (or sourcing untrusted quantum states) are detected and appropriately mitigated (Sutradhar, 17 Jan 2025, Hayashi et al., 2019).

Device independence, unconditional secrecy under collusion, and post-quantum security (semantic security under quantum attacks) are achieved in specific QSA constructions via quantum self-testing, entanglement monogamy, and hardness assumptions (Module-LWE, LPN) (Hayashi et al., 2019, Bitzer et al., 19 Jan 2026).

2. Protocol Paradigms: GHZ, Cat, Homomorphic, and Masking Approaches

QSA protocols are classifiable by the quantum resources and operational flows they employ. The following table summarizes key protocol categories:

Protocol Type	Core Quantum Resource	Aggregation Mechanism
Entanglement-based	GHZ/cat state distribution	Phase encoding, interference, parity check
Homomorphic encryption	Pauli/CNOT masking, QHE	Clifford (or lattice/code-based) additivity
Threshold sharing	Polynomial secret sharing	QFT/qudit shifting with Lagrange weights

GHZ/cat-state phase aggregation protocols create multipartite entanglement across all parties (GHZ: $$|GHZ_n\rangle = \frac{1}{\sqrt{2}} (|0\rangle^{\otimes n} + |1\rangle^{\otimes n})$$). Each participant encodes their data by a local phase rotation (e.g., $R_Z(\theta_i)$), then aggregation and decoding are achieved by interference and measurement, yielding the global sum while keeping individual phase contributions hidden (Zhang et al., 2022, Ampatzis et al., 2022).

Quantum secret sharing and threshold schemes employ classical Shamir's secret sharing over a prime field combined with quantum preprocessing: entangled qudit distribution, QFT operation, and modular shifts. These $(t,n)$-threshold subprotocols ensure that only qualified subsets of size $t\leq n$ reconstruct the aggregate, with strict privacy against collusions below threshold (Sutradhar, 17 Jan 2025).

Quantum homomorphic encryption encapsulates private inputs within quantum-masked states. Evaluation is performed by Clifford operations (notably Pauli and CNOT, avoiding expensive $T$/phase gates). Set cardinality protocols use these primitives to compute intersection and union cardinality without learning anything else, relying on Pauli-masking and secure CNOT logic (Ye et al., 2024).

Post-quantum secure aggregation protocols use public-key encryption schemes (CRYSTALS-Kyber Module-LWE (Rahmati et al., 3 Jan 2026), LPN-based code homomorphic (Bitzer et al., 19 Jan 2026)) to generate per-client one-time pad masks for input vectors. These are added in such a way that masks cancel on aggregation, revealing only the sum, yet remaining secure even to quantum adversaries.

3. Security Models, Threat Characterization, and Verification

QSA protocol design mandates explicit adversary modeling—ranging from honest-but-curious semi-trusted parties, active internal colluders, byzantine attackers seeking to corrupt the aggregate, to external quantum eavesdroppers. Core threat resilience mechanisms include:

• Intercept–Resend Detection: Use of basis-randomized decoy states and parity checks guarantees high-probability detection of channel attacks via error estimation (Ampatzis et al., 2022, Chang et al., 2021, Zhang et al., 2022).
• Non-collusion and Verifiability: Device-independent self-testing protocols (GHZ self-test with statistical significance) allow each participant to locally certify the correct entangled state preparation and global secrecy, achieving quantitative $\varepsilon$-security for up to $m-2$ colluders (Hayashi et al., 2019).
• Post-Quantum Resilience: Aggregation schemes based on CRYSTALS-Kyber and LPN exploit computational hardness against Shor's and quantum information-set decoding attacks. Mask sharing and dropout mitigation with Shamir's secret sharing increase resilience in federated settings (Rahmati et al., 3 Jan 2026, Bitzer et al., 19 Jan 2026).
• Information-theoretic Secrecy: Quantum entanglement (GHZ monogamy, phase superposition) and Pauli-twirl masking deliver unconditional privacy; no side information beyond the global sum leaks to any adversary (Ampatzis et al., 2022, Sutradhar, 17 Jan 2025).

Leakage quantification is provided in terms of mutual information and trace-norm closeness to ideal randomness (e.g., Holevo and Cramér–Rao bounds for continuous-variable photonic protocols) (Sulimany et al., 2024).

4. Resource, Communication, and Efficiency Analysis

Quantum Secure Aggregation schemes exhibit diverse resource costs dependent on chosen primitives:

• Quantum resources: Number of entangled qubits/qudits (GHZ size), rounds of quantum distribution, necessity for quantum repeaters in large networks, and error tolerance during noisy transmission (Sutradhar, 17 Jan 2025, Zhang et al., 2022).
• Classical communication: For threshold or masking schemes: secret-shares, broadcasted masked outputs, local verification bits. Quantum homomorphic variants require transmission of masked quantum states and possible committee-based decryption shares (Ye et al., 2024, Bitzer et al., 19 Jan 2026).
• Computation: Resource overhead proportional to participant number ($O(n)$ for secret-sharing interpolation, gates per quantum participant), and polynomial complexity in code-based or lattice-based cryptosystems (Rahmati et al., 3 Jan 2026).

Experimental benchmarks confirm practical aggregation latency (sub-second in federated threat intelligence sharing), competitive communication overhead (<4% beyond vanilla aggregation), and empirical accuracy exceeding 96% in federated learning contexts—showing only marginal model utility loss at security parameters matching classical deployments (Zhang et al., 2022, Rahmati et al., 3 Jan 2026).

5. Federated Learning, Sensor Networks, and Applied QSA Protocols

QSA has been deployed in multiple real-world privacy-critical settings:

• Federated Quantum Machine Learning: Aggregation of local gradient updates, weights, or measurement statistics, applying either phase-encoded qubit aggregation (GHZ superposition) or classical-to-quantum secret-sharing schemes. MNIST and CIFAR-10 tests show full privacy with utility-preserving aggregation (Zhang et al., 2022, Sulimany et al., 2024, Rahmati et al., 3 Jan 2026).
• Secure Voting and Sensor Data Fusion: Weighted voting and distributed measurement aggregation apply threshold QSMS and entanglement-swapping approaches to ensure only the global tally is revealed (Sutradhar, 17 Jan 2025, Chang et al., 2021).
• Private Set Intersection/Union Cardinality: Quantum homomorphic set protocols enable computation of intersection and union sizes with only Pauli and CNOT gates, scaling efficiently for multi-party scenarios without full entanglement resources (Ye et al., 2024).
• Critical Infrastructure IoT: Real-time threat intelligence sharing aggregates model updates over CRYSTALS-Kyber masking, Byzantine-robust aggregation, and dynamic client reputation-based selection, maintaining differential privacy guarantees (Rahmati et al., 3 Jan 2026).

6. Limitations, Open Problems, and Research Directions

Present QSA frameworks face diverse implementation, scalability, and robustness challenges:

• Fault Tolerance: Quantum protocols in NISQ-era hardware suffer from error accumulation and decoherence, limiting reliable entanglement distribution over large networks (Sutradhar, 17 Jan 2025, Zhang et al., 2022).
• High-Dimensional Model Support: Encoding multidimensional deep network parameter vectors may require batched or parallel GHZ entanglement, Clifford-circuit optimizations, or multiplexed phase encoding (Zhang et al., 2022).
• Dropout and Dynamic Participation: Real-world federated aggregation necessitates robust mask-recovery schemes (e.g., Shamir secret sharing) in the face of client dropout (Rahmati et al., 3 Jan 2026).
• Extension to Richer Aggregates: Non-linear functions (e.g., multiplication, inner product, circuit evaluation) require advanced entanglement and interaction patterns, such as multi-party graph states, gate teleportation, or fully homomorphic quantum schemes (Ye et al., 2024, Ouyang et al., 2017).
• Post-Quantum Assumption Formalization: Code-based schemes (LPN hardness, Hint-LPN reduction) and committee-based decryptors are new directions with open parameterization and performance trade-off analyses (Bitzer et al., 19 Jan 2026).

Future research focuses on hybrid classical–quantum aggregation, scalable quantum network deployment, tighter secrecy bounds under quantum-advanced adversaries, and generalization to threshold schemes under dynamic party sets.

7. Synthesis and Landscape Position

Quantum Secure Aggregation protocols unify quantum secret sharing, entanglement-assisted masking, and post-quantum cryptography into an operational framework that exceeds classical information-theoretic and computational privacy capabilities. QSA achieves the following advances:

• Device- and information-theoretic secrecy against broad adversary classes—including quantum attackers—using phase encoding, GHZ/cat-state monogamy, and computational masking.
• Flexible threshold aggregation, scalable to large networks and tolerant of dropouts/collusion.
• **Cryptographic primitives facilitating federated learning, private voting, sensor fusion, and collaborative analytics, with experimentally validated efficiency and utility preservation.
• Provable quantitative bounds on input and model leakage, robust authorization and selection mechanisms, and interoperability with current quantum and classical communication infrastructure.

QSA continues to evolve as a pivotal field for privacy- and security-critical distributed computation, at the nexus of quantum information science and advanced cryptography.

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References: Sutradhar (QSMS protocol) (Sutradhar, 17 Jan 2025); Hayashi & Koshiba (verifiable QSA) (Hayashi et al., 2019); Zhang et al. (entanglement-swapping) (Chang et al., 2021); Sulimany et al. (photonic linear algebra engine) (Sulimany et al., 2024); Ampatzis & Andronikos (GHZ-agent protocol) (Ampatzis et al., 2022); CRYSTALS-Kyber QSA (Rahmati et al., 3 Jan 2026); Code-based LPN QSA (Bitzer et al., 19 Jan 2026); Federated quantum aggregation (Zhang et al., 2022).