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Semi-Quantum Conference Key Agreement with GHZ-type states

Rúben Barreiro, Walter O. Krawec, Paulo Mateus, Nikola Paunković, André Souto

TL;DR

The paper addresses secure multiparty key distribution in a semi-quantum setting by introducing a SQCKA protocol that uses GHZ-type states with one fully quantum party and $n$ semi-quantum Bobs, without a trusted mediator. It provides an information-theoretic security proof against collective attacks in the asymptotic limit and derives a computable key-rate bound $r \ge S(A|E)_{\rho} - \max_j H(A|B_j)$, supplemented by a bound on $S(A|E)_{\rho}$ and a depolarising-channel analysis. The contributions include a detailed protocol description, a state-evolution security framework, parameter estimation schemes, and explicit depolarising-noise-based key-rate expressions for any number of parties, supported by numerical insights. The work advances practical SQCKA by reducing resource needs and eliminating mediator trust, and it sets the stage for future extensions to stand-alone, device-independent, and composable security, as well as experimental validation.

Abstract

We propose a semi-quantum conference key agreement (SQCKA) protocol that leverages on GHZ states. We provide a comprehensive security analysis for our protocol that does not rely on a trusted mediator party. We present information-theoretic security proof, addressing collective attacks within the asymptotic limit of infinitely many rounds. This assumption is practical, as participants can monitor and abort the protocol if deviations from expected noise patterns occur. This advancement enhances the feasibility of SQCKA protocols for real-world applications, ensuring strong security without complex network topologies or third-party trust.

Semi-Quantum Conference Key Agreement with GHZ-type states

TL;DR

The paper addresses secure multiparty key distribution in a semi-quantum setting by introducing a SQCKA protocol that uses GHZ-type states with one fully quantum party and semi-quantum Bobs, without a trusted mediator. It provides an information-theoretic security proof against collective attacks in the asymptotic limit and derives a computable key-rate bound , supplemented by a bound on and a depolarising-channel analysis. The contributions include a detailed protocol description, a state-evolution security framework, parameter estimation schemes, and explicit depolarising-noise-based key-rate expressions for any number of parties, supported by numerical insights. The work advances practical SQCKA by reducing resource needs and eliminating mediator trust, and it sets the stage for future extensions to stand-alone, device-independent, and composable security, as well as experimental validation.

Abstract

We propose a semi-quantum conference key agreement (SQCKA) protocol that leverages on GHZ states. We provide a comprehensive security analysis for our protocol that does not rely on a trusted mediator party. We present information-theoretic security proof, addressing collective attacks within the asymptotic limit of infinitely many rounds. This assumption is practical, as participants can monitor and abort the protocol if deviations from expected noise patterns occur. This advancement enhances the feasibility of SQCKA protocols for real-world applications, ensuring strong security without complex network topologies or third-party trust.

Paper Structure

This paper contains 11 sections, 2 theorems, 63 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The proposed semi-quantum conference key agreement protocol
  4. Security proof
  5. State evolution
  6. Parameter estimation
  7. Entropy evaluation
  8. Noise evaluation -- depolarising channel
  9. Case of reflection:
  10. Case of measurment:
  11. Conclusions

Key Result

Theorem 1

(From QKD-Tom-Krawec-Arbitrary): Let $\rho_{AE}$ be a quantum state of the form: where $\mathcal{N}$ is a normalization constant, $\ket{E_i^a}$ are in general neither normalized nor mutually orthogonal vectors. Then, the von Neumann entropy $S(A|E)_\rho$ may be bounded by where where $H(\lambda)$ is the Shannon entropy of the binary distribution $\{\lambda, 1-\lambda\}$ and $E_i^0$ and $E_i^0$

Figures (4)

  • Figure 1: Schematic drawing of our proposal for a single round. In the beginning, Alice prepares a GHZ state with $n$+1 particles and sends one particle of that state to each of $n$ Bob's (full arrows). Using a pre-shared key, each Bob decides to Reflect (R) the state or Measure and Resend (MR) back the outcome as a state (dashed arrows). When Alice receives all the states from Bob, she either confirms that she has GHZ state in the first case or measures her qubit and compares it to all the other outcomes of measuring the remaining ones in the computational basis.
  • Figure 2: Key rate lower bounds for depolarization channel with $n=10$ Bobs.
  • Figure 3: Key rate lower bounds for depolarization channel for several number $n$ of Bobs with $Q = \widetilde{Q}$.
  • Figure 4: Key rate lower bounds for depolarization channel for several number $n$ of Bobs with (a) $Q=0$, and (b) $\widetilde{Q} = 0$.

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • proof