Quantum Dining Information Brokers Problem

• Quantum Dining Information Brokers Problem is a quantum protocol enabling spatially separated brokers to simultaneously share private data while preserving anonymity.
• It utilizes maximally entangled GHZ states and unitary operations to encode secrets, with a random permutation process ensuring robust privacy and untraceability.
• This approach underpins advanced applications such as anonymous multiparty data sharing, secure distributed voting, and privacy-preserving collaborative computation.

The Quantum Dining Information Brokers Problem (QDIBP) is a quantum information-theoretic extension of anonymous information exchange, formulated for a network of spatially separated brokers who wish to simultaneously share private data while preserving the anonymity and privacy of all participants. The QDIBP generalizes principles of secure multiparty protocols—particularly the dining cryptographers problem—to the setting where all participants are both senders and receivers, requiring a fully parallel, many-to-many, anonymous communication with strong privacy guarantees and scalability in distributed systems (Andronikos et al., 18 Jul 2025).

1. Problem Definition and Conceptual Framework

The QDIBP envisions $n$ information brokers, each located in distinct geographic regions, engaging in a metaphorical “virtual dinner” during which every broker wishes to share a unique secret (bit string or block) with all others at the same time. The primary objectives are:

• Parallelism: All brokers transmit and receive their information simultaneously in a single communication phase, in contrast with iterative or sequential schemes.
• Anonymity: Each recipient obtains the information without being able to attribute it to a particular sender.
• Privacy and Untraceability: No participant learns anything beyond the received messages; no party, including the aggregating third party (if any), can match secrets to brokers.
• Scalability and Distribution: The protocol must operate under full spatial separation (brokers can be anywhere in the world) with resource scalability for both large $n$ and message sizes.

The QDIBP thus serves as an archetype for secure, scalable, and privacy-preserving information exchange in quantum networks, with foundational implications for quantum communication, cryptography, distributed computing, and privacy engineering (Andronikos et al., 18 Jul 2025).

2. Quantum Protocol Architecture

The core protocol employs maximally entangled Greenberger–Horne–Zeilinger (GHZ) states over multiple qubits and leverages quantum parallelism and the no-cloning property to enable simultaneous, anonymous communication:

1. Entanglement Resource: Each broker receives a quantum register (multi-qubit) from a globally prepared $r$-qubit or $r \cdot p$-qubit GHZ state:

$$\lvert \text{GHZ}_r \rangle = \frac{1}{\sqrt{2}} (|0\ldots0\rangle + |1\ldots1\rangle)$$

or in the resource-rich setting,

$$\lvert \text{GHZ}_r \rangle^{\otimes p} = 2^{-p/2} \sum_{x \in \mathbb{B}^p} |x\rangle_{r-1} \cdots |x\rangle_0$$

1. Encoding: Each broker encodes their secret $\tilde{s}_i$ (a bit vector of length $m$) into the relative phase of their local register by applying a unitary transformation:

$$U_{\tilde{s}_i} : |-\rangle|x\rangle \to (-1)^{\tilde{s}_i \cdot x} |-\rangle |x\rangle$$

Here, the dot denotes the bitwise inner product modulo 2.

1. Measurement and Aggregation: All brokers then perform measurements in the Hadamard basis $H^{\otimes p}$. Each sends their outcomes to a semi-honest, non-colluding third party, Trent, who computes the aggregated secret (the blockwise XOR of all submitted secrets):

$$t = \tilde{s}_0 \oplus \tilde{s}_1 \oplus \ldots \oplus \tilde{s}_{n-1}$$

1. Random Permutation and Obfuscation: To preserve untraceability, Trent applies a random permutation $\sigma_i$ independently to each block within every segment of the aggregated vector, reshuffling the aggregated data before broadcasting the result back to all brokers.
2. Decoding: Each broker, using their own secret and the permutation information, can extract the messages sent by all others, while the permutation step rigorously obscures the association between any block and its author (Andronikos et al., 18 Jul 2025).

3. Anonymity, Privacy, and Security Properties

The QDIBP protocol achieves several strong cryptographic guarantees:

• Perfect Sender Anonymity: The global phase encoding and post-processing random permutation ensure that no broker can infer the identity of the sender corresponding to any message block. Structural anonymity is preserved in the aggregated secret since no positional metadata is retained after permutation (Andronikos et al., 18 Jul 2025).
• Untraceability: Receipt of a particular information block cannot be attributed to any participant by analysis of quantum or classical channels, even in the presence of full observational access by the third-party aggregator.
• Simultaneity and Parallelism: All brokers’ contributions are encoded and processed in a single round, achieving information-theoretic simultaneity.
• Robustness Against Collusion and Semi-Honest Adversaries: Privacy guarantees hold so long as Trent or the brokers do not collude; the protocol assumes at least one honest party in the role of the third party for full anonymity.
• Security Relies on GHZ-Correlated Measurement: The only valid aggregated secret emerges if all brokers perform private operations and measurements according to the Hadamard entanglement property. Any attempt to cheat or diverge from the protocol can be detected due to the structure of measurement outcomes after permutation and public comparison.

4. Scalability and Implementation Considerations

The QDIBP protocol achieves scalability via the following mechanisms:

Resource/Aspect	Scaling Principle	Implementation Note
Number of brokers $n$	Protocol supports unbounded $n$	Each broker’s register size grows with $n^2 m$
Message size $m$	Supports arbitrarily large $m$	Multiple blocks handled in a parallel circuit array
Quantum gates	Hadamard and CNOT	Readily implementable on modern quantum devices
Spatial Distribution	Entanglement distance-invariant	Brokers can operate at arbitrary global locations

While the exponential scaling of quantum resources with respect to $n$ and $m$ represents a practical challenge for very large networks, for modestly sized broker collectives and moderate message sizes, the protocol is directly implementable using current quantum computing architectures. All brokers execute identical modular quantum circuits, simplifying deployment and error analysis (Karananou et al., 30 Jan 2024, Andronikos et al., 18 Jul 2025).

5. Comparison to Classical Anonymous Information Exchange

The QDIBP represents a significant advance over classical and earlier quantum protocols:

• Classical dining cryptographers protocols achieve one-to-many or single-bit anonymity but require sequential rounds for many-to-many communication. Collisions or disruptors in the network can degrade anonymity, and full parallelism is not ensured (Franck et al., 2014, Mödinger et al., 2021).
• Sequential one-to-many quantum extensions for e.g., anonymous broadcast or vote casting do not guarantee the sender anonymity of simultaneous many-to-many exchange, as the identity of message originators can sometimes be reconstructed by analyzing round orderings or content correlations (Hameedi et al., 2017).
• Quantum Dining Information Brokers Protocol overcomes these limitations by embedding all contributions into a global, randomly permuted aggregated secret produced in a single round, with mutual privacy and anonymity for all senders (Andronikos et al., 18 Jul 2025).

The table below highlights key features:

Feature	Classical DCN	Sequential Quantum	QDIBP
Many-to-many exchange	No	No	Yes
Parallelism (single-step)	No	No	Yes
Sender anonymity	Partial	Partial	Complete
Scalability	Variable	Limited	Explicitly scalable
Distributed operation	Possible	Yes	Yes

6. Broader Applications and Theoretical Significance

The QDIBP and its underlying entanglement-based mechanisms have broad application prospects:

• Anonymous multiparty data sharing: Secure and untraceable exchange of sensitive datasets between institutions, such as distributed healthcare, governance, or finance.
• Distributed voting and consensus: Unconditional privacy-preserving voting in e-democracy systems, including applications in blockchains and distributed ledgers.
• Collaborative computation: Privacy-preserving aggregation of intermediate computations from spatially distributed agents.
• Quantum data markets and brokerage: As quantum data exhibits consumability and rivalness due to measurement-induced destruction (Gilboa et al., 13 Sep 2024), the QDIBP establishes an architectural foundation for economic transactions where information access and privacy controls are implemented through quantum resources.

Finally, the QDIBP exemplifies the intersection of quantum information theory, privacy engineering, and distributed computation. By leveraging high-dimensional multipartite entanglement, relative phase encoding, and permutation-based obfuscation, it yields an extensible solution for secure, anonymous, and massive parallel communication in future quantum networks (Andronikos et al., 18 Jul 2025, Karananou et al., 30 Jan 2024, Gilboa et al., 13 Sep 2024).