Quantum Shadows: The Dining Information Brokers

TL;DR

This paper introduces the Quantum Dining Information Brokers Problem (QDIBP), a distributed, entanglement-based protocol enabling fully parallel, anonymous, many-to-many information exchange among $n$ brokers in geographically separated locations. The approach builds on the Dining Cryptographers Problem and prior quantum anonymity schemes, adopting a three-phase protocol (phase 1: distribute/obfuscate secrets via phase-encoding in a GHZ-based entangled system; phase 2: shuffle blocks within segments to preserve sender anonymity; phase 3: disseminate aggregated information encoded in relative phases) that leverages an $r$-uniform entanglement distribution scheme. Key contributions include achieving many-to-many simultaneous communication, guaranteed anonymity/untraceability of senders, and a fully distributed framework compatible with current quantum networks, at the cost of substantial qubit resources on the order of $n^2 m$. The framework is demonstrated through a small-scale realization with a three-broker example, illustrating the encoding, permutation, and retrieval steps and showcasing the protocol's viability for privacy-preserving distributed data exchange.

Abstract

This article introduces the innovative Quantum Dining Information Brokers Problem, presenting a novel entanglement-based quantum protocol to address it. The scenario involves $n$ information brokers, all located in distinct geographical regions, engaging in a metaphorical virtual dinner. The objective is for each broker to share a unique piece of information with all others simultaneously. Unlike previous approaches, this protocol enables a fully parallel, single-step communication exchange among all brokers, regardless of their physical locations. A key feature of this protocol is its ability to ensure both the anonymity and privacy of all participants are preserved, meaning no broker can discern the identity of the sender behind any received information. At its core, the Quantum Dining Information Brokers Problem serves as a conceptual framework for achieving anonymous, untraceable, and massively parallel information exchange in a distributed system. The proposed protocol introduces three significant advancements. First, while quantum protocols for one-to-many simultaneous information transmission have been developed, this is, to the best of our knowledge, one of the first quantum protocols to facilitate many-to-many simultaneous information exchange. Second, it guarantees complete anonymity and untraceability for all senders, a critical improvement over sequential applications of one-to-many protocols, which fail to ensure such robust anonymity. Third, leveraging quantum entanglement, the protocol operates in a fully distributed manner, accommodating brokers in diverse spatial locations. This approach marks a substantial advancement in secure, scalable, and anonymous communication, with potential applications in distributed environments where privacy and parallelism are paramount.

Figures (13)

• Figure 1: This figure gives a pictorial representation of the structure of the extended secret information vectors $\widetilde{ \mathbf{ s } }_{ 0 }$, $\dots$, $\widetilde{ \mathbf{ s } }_{ n - 1 }$.
• Figure 2: This figure shows the construction of the primary segments $\mathbf{ p }_{ 0 }$, $\dots$, $\mathbf{ p }_{ n - 1 }$.
• Figure 3: This figure depicts the construction of the auxiliary segments $\mathbf{ a }_{ 0 }$, $\dots$, $\mathbf{ a }_{ n - 1 }$.
• Figure 4: This figure gives a pictorial representation of the structure of the extended secret information vectors $\widetilde{ \mathbf{ s } }_{ 0 }$, $\dots$, $\widetilde{ \mathbf{ s } }_{ n - 1 }$.
• Figure 5: This figure provides a detailed and analytical depiction of the extended secret information vectors $\widetilde{ \mathbf{ s } }_{ 0 }$, $\dots$, $\widetilde{ \mathbf{ s } }_{ n - 1 }$, expressed in terms of their constituent blocks. We clarify that the blocks drawn in green contain the zero vector $\mathbf{ 0 }_{ m }$, while blocks drawn in blue contain secret vectors.

Theorems & Definitions (9)

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