⚛️ quantum physics

High-rate multipartite quantum secret sharing with composable security

This paper experimentally demonstrates a high-rate, composable-secure multipartite quantum secret sharing protocol using 4-qubit GHZ states distributed over a 20-km fiber network, achieving a secret key rate of 750 bits per second and projecting a 24-hour secure key yield of 8.7 Mbits while providing robust security against general and participant attacks.

Original authors: Russell M. J. Brooks, Joseph Ho, Joseph Niblo, Janka Memmen, Anna Pappa, Jens Eisert, Nathan Walk, Alessandro Fedrizzi

Published 2026-09-15

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CC BY 4.0

Original authors: Russell M. J. Brooks, Joseph Ho, Joseph Niblo, Janka Memmen, Anna Pappa, Jens Eisert, Nathan Walk, Alessandro Fedrizzi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the future, the internet may evolve into something far more secure than the networks we use today, relying on the strange rules of quantum physics to protect information. At the heart of this potential revolution is a concept called quantum secret sharing. Imagine a vault that cannot be opened unless a specific group of people works together; if even one person is missing, the secret remains locked away. This is the essence of secret sharing, a method used to distribute a piece of information among many people so that only an authorized team can reconstruct it. While classical versions of this exist, they rely on mathematical complexity that could one day be broken by powerful computers. Quantum secret sharing offers a different path, using the fundamental laws of nature to detect if anyone is trying to eavesdrop or act dishonestly. The challenge has been making this work in the real world, especially when dealing with multiple people who might not trust each other, and ensuring the system remains secure even when the number of data points collected is limited.

A team of researchers has now taken a significant step forward by demonstrating a working version of this technology that is both fast and rigorously secure. They built an experiment to test a protocol where a central dealer distributes a secret to a group of participants, ensuring that the secret can only be recovered if everyone in the group collaborates. The researchers used light particles, specifically photons, to carry the information. They generated a special state of four photons that were linked together in a way that defies classical intuition; measuring one instantly affects the others, no matter how far apart they are. This linked state, known as a GHZ state, served as the vehicle for the secret. The team managed to create these four-photon links at a rate of over five thousand times per second, a speed that is remarkably high for such complex quantum states.

The experiment was designed to test not just the speed, but the security against a specific type of threat: a dishonest participant. In many previous attempts, a single untrustworthy person in the group could potentially learn the secret without helping the others, simply by manipulating the order of their actions. The researchers implemented a new method that prevents this. By carefully analyzing the data from their measurements, they inferred that the system would protect the secret even if one or more participants tried to act dishonestly, under the assumption that the source and device statistics remain stationary. They distributed these linked photons through a network of optical fibers totaling twenty kilometers in length, simulating a real-world connection between a central server and three different users. The setup was a star shape, with the source in the middle and the users at the ends of the arms.

Over the course of ten hours of laboratory time, the team collected millions of measurement events. They analyzed the errors and the rates at which the photons arrived to calculate how much secret information could be safely extracted. The results showed that the system could generate a secure key at a rate of about 750 bits per second in an ideal, infinite scenario. More importantly, when they accounted for the fact that they only had a finite amount of data, their calculations showed that a full day of running this optimized system would yield a secure secret of nearly nine million bits. This lower bound confirms that the protocol is not only theoretically sound but practically viable for generating substantial amounts of secure data, provided the system operates with genuine random basis selection.

The researchers also addressed the issue of efficiency. In earlier versions of such protocols, the participants had to choose their measurement settings randomly and equally, which wasted a lot of potential data because the settings often did not match. The team showed that by slightly biasing the choice of settings toward the most useful configuration, they could dramatically increase the amount of secret key generated without compromising security. This optimization allowed them to reach an efficiency comparable to the most trusted communication methods, but with the added safety of detecting dishonest participants. The experiment relied on high-quality crystals to create the photons and superconducting detectors to count them, ensuring that the noise in the system remained low enough to maintain the integrity of the secret.

While this demonstration is a proof of principle, it highlights the path toward a future where quantum networks can securely coordinate groups of people. The researchers noted that scaling this up to larger networks will require even more advanced sources of light and better ways to handle the loss of photons over long distances. They also pointed out that their current setup used motorized devices to switch measurement settings in blocks, which is slower than what a fully secure, real-time system would need. Specifically, the blockwise acquisition used in the experiment does not reproduce the adversarial random-sampling condition required for composable security against general attacks; the reported values should therefore be interpreted as a performance projection for an implementation with genuine random basis selection. However, the data collected provides a solid benchmark for what is possible. By combining high-speed generation with a rigorous security analysis that accounts for finite data and dishonest users, this work moves quantum secret sharing from a theoretical idea into a tangible reality, offering a new standard for how groups might share secrets in a connected world.

Technical Summary: High-rate multipartite quantum secret sharing with composable security

Problem Statement
Quantum secret sharing (QSS) is a cryptographic primitive designed to distribute information among $n$ parties such that only authorized subsets of size $k$ can reconstruct the secret. While early protocols, such as the Hillery-Bužek-Berthiaume (HBB) scheme based on Greenberger-Horne-Zeilinger (GHZ) states, demonstrated the feasibility of using multipartite entanglement for secure distribution, they faced significant security vulnerabilities. Specifically, canonical GHZ-based protocols are susceptible to "participant attacks," where dishonest participants attempt to learn the secret without collaborating. Previous attempts to mitigate this, such as randomizing response orders or treating unauthorized subsets as adversaries, were often limited to the asymptotic limit (infinite rounds) or failed to provide finite-key security with positive key rates when applied to the HBB protocol. Furthermore, existing demonstrations often lacked composable security guarantees, which are essential for integrating QSS into broader cryptographic networks.

Methodology
This work experimentally evaluates a discrete-variable $(n, n)$ -threshold QSS protocol that offers composable security against general attacks, including participant attacks. The protocol relies on a measurement scheme that establishes pairwise correlations between the dealer (Alice) and each participant (Bob), allowing the information leakage to be bounded using entropic uncertainty relations.

The experimental setup utilizes a linear optics architecture to generate four-qubit GHZ states. Two domain-engineered entangled photon-pair sources (EPS), pumped by a 775 nm picosecond pulsed laser, produce photon pairs at 1550 nm via spontaneous parametric down-conversion (SPDC). The sources employ aperiodically-poled potassium titanyl phosphate (AKTP) crystals within Sagnac interferometers to ensure spectrally pure biphoton states. Entanglement is generated by interfering one photon from each source on a polarizing beamsplitter, post-selecting for the four-qubit GHZ state $|GHZ\rangle = (|h,h,h,h\rangle + e^{i\phi}|v,v,v,v\rangle)/\sqrt{2}$ .

The protocol involves distributing these states to a dealer and three participants over a 20 km fiber network (configured as a 4-arm star topology with 5 km links per user). Users perform measurements in randomly chosen Pauli-Z or Pauli-X bases. Rounds where all users measure in the X basis are used for key generation, while rounds involving Z measurements by the dealer and at least one participant serve as check rounds for parameter estimation. The authors apply a finite-key analysis to the experimental data, utilizing Hoeffding and Serfling bounds to account for finite-size sampling effects and optimize the basis probability to maximize the secret key rate.

Key Contributions and Results

High-Rate Generation: The experiment achieved a four-fold generation rate exceeding $5 \times 10^3$ events per second (specifically 5025 counts/s) with a state fidelity of $0.842 \pm 0.002$ .
Asymptotic Key Rate: Under optimal pump power (600 mW) and zero transmission loss conditions, the system demonstrated an asymptotic extractable secret-key rate of $750 \pm 10$ bits per second.
Network Demonstration: The protocol was successfully executed over a 20 km fiber network. Despite a total loss of approximately 5 dB, the system maintained an average four-fold rate of 1197 counts/s with error rates of $Q_X = 0.090 \pm 0.003$ and $\max[Q_{A,B_i}] = 0.075 \pm 0.001$ .
Composable Finite-Key Security: By applying finite-key analysis to the measured statistics, the authors inferred that a randomized 24-hour execution with optimized basis bias would yield a composable finite-key lower bound of 8.7 Mbits. This represents a significant improvement over unoptimized symmetric basis probabilities, which yield a lower bound of $7.4 \times 10^5$ bits.
Basis Bias Optimization: The work demonstrates that biasing measurement probabilities (favoring the key-generation basis) can be implemented without compromising security against participant attacks, achieving asymptotic efficiency comparable to trusted quantum key distribution (QKD) protocols.

Significance and Claims
The paper positions this work as a proof-of-principle demonstration that bridges the gap between theoretical composable security and practical high-rate multipartite quantum cryptography. The authors claim that their implementation provides a new benchmark for QSS key rates, comparable to leading experiments in four-photon GHZ generation and fidelity.

Crucially, the work establishes that composable security against participant attacks is achievable in the discrete-variable regime with finite-key effects, resolving a challenge that previously limited the practical deployment of HBB-style protocols. The authors note that while the current experiment uses motorized analyzers that record settings in blocks (rather than independent random selection per round), the results serve as a valid performance projection for a fully cryptographic implementation with genuine random basis selection, assuming stationary source and device statistics.

The authors conclude that scaling this technology to larger networks will require advancements in near-deterministic sources (such as quantum dots) and entanglement gates, or the use of time-multiplexed probabilistic sources. They also identify the extension of this framework to quantum state sharing and general $(k, n)$ -threshold schemes using graph states as a natural next step for enabling flexible access structures in distributed quantum computing and consensus protocols.

Technical Summary: High-rate multipartite quantum secret sharing with composable security

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