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Quantum Key Distribution in Multi-Valued Logic: Using Entangled Qutrits for Unconditional Security

Wajdi Sabah Abdul Razzaq

Published May 12, 2026• 0 citations
Publisher

Abstract

This paper presents two novel quantum key distribution (QKD) protocols operating in three-valued (qutrit-based) logic. Protocol I demonstrates a simplified QKD scheme that avoids quantum qubit transmission, relying instead on entangled qutrit pairs to achieve unconditional security between one sender and one receiver. Protocol II generalises this framework to n = 3^m receivers using a maximally entangled (m+n)-qutrit state. The key efficiency η = (n+1)/(n+m) exceeds 50% and improves with the number of users. Both protocols achieve unconditional security. This work constitutes the first reported QKD protocol designed natively for three-valued quantum logic.

DOI
10.5281/zenodo.20137198

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This paper presents two novel quantum key distribution (QKD) protocols operating in three-valued (qutrit-based) logic. Protocol I demonstrates a simplified QKD scheme that avoids quantum qubit transmission, relying instead on entangled qutrit pairs to achieve unconditional security between one sender and one receiver. Protocol II generalises this framework to n = 3^m receivers using a maximally entangled (m+n)-qutrit state. The key efficiency η = (n+1)/(n+m) exceeds 50% and improves with the number of users. Both protocols achieve unconditional security. This work constitutes the first reported QKD protocol designed natively for three-valued quantum logic.
Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the Bennett-Brassard 1984 and Bennett 1992 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three-state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has been shown only for the trivial intercept-resend eavesdropping strategy. In this Letter, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.
Quantum key distribution (QKD) refers to specific quantum strategies which permit the secure distribution of a secret key between two parties that wish to communicate secretly. Quantum cryptography has proven unconditionally secure in ideal scenarios and has been successfully implemented using quantum states with finite (discrete) as well as infinite (continuous) degrees of freedom. Here, we analyze the efficiency of QKD protocols that use as a resource entangled gaussian states and gaussian operations only. In this framework, it has already been shown that QKD is possible [1] but the issue of its efficiency has not been considered. We propose a figure of merit (the efficiency E) to quantify the number of classical correlated bits that can be used to distill a key from a sample of N entangled states. We relate the efficiency of the protocol to the entanglement and purity of the states shared between the parties.
This paper investigates the optimization of Quantum Key Distribution (QKD) protocols utilizing entangled states. The core claim is that strategic optimization of entangled state generation and utilization can significantly enhance the security and key rate of QKD. The proposed method leverages principles from quantum information theory and entanglement theory to design a protocol that maximizes key distribution speed while minimizing the risk of key leakage. Current QKD protocols predominantly rely on single photons, often neglecting the full potential of entangled states. This work addresses this limitation, aiming to improve the efficiency and security of quantum key distribution. The presented protocol incorporates techniques for enhanced entanglement distribution, error correction, and privacy amplification, all tailored for maximizing key rate within a secure framework. Mathematical analysis and theoretical considerations are detailed throughout, outlining the protocol's operational parameters and security proofs. The ultimate goal is to demonstrate a more robust and efficient approach to QKD based on the fundamental properties of entanglement. ---
Abstract Since the 80 s when it was first proposed, Quantum Key Distribution (QKD) elicited great interest in the field of cryptography as a unique procedure for key generation that could in principle guarantee unconditionally secure communication “by the laws of Physics”. In the last fifteen years commercial solutions have started appearing on the market, showing that practical implementations of the protocol were not only possible but also competitive in terms of security and achievable secret-key rate. In this work we describe a simulation of the historical QKD protocol E91 on the IBM Quantum platform, making use of the qubit formalism to represent the quantum states received by two communicating nodes. Having implemented also the post-processing steps for the error correction and the privacy amplification, this model can represent a simple stand-alone tool to study the performance not only of one-to-one communication but of more complex systems that rely on QKD for security, one above all QKD networks.
Most prior semi-quantum key distribution (SQKD) protocols are designed in the context of qubits. In this paper, we proposed an SQKD protocol using ([Formula: see text]+1) quantum states in two mutually unbiased bases in the context of qudits without invoking the classical party’s measurement capability. It not only decreases the quantum states sent by quantum party by half, but also improves the efficiency of key rate than qubits do. To prove the security of present protocol, we first illustrate that the present protocol is completely robust, and then prove its unconditional security from information theoretical perspective by computing its key rate and noise tolerance against cloning-based individual attack. The unconditional security proof demonstrates that the higher dimension of quantum system is, the higher key rate can be obtained and the higher noise tolerance is allowed in depolarization channel.