[Paper Review] A qutrit Quantum Key Distribution protocol with better noise resistance

Franc̨ois Arnault, Zoé Amblard|arXiv (Cornell University)|Apr 16, 2014

Quantum Mechanics and Applications1 references3 citations

TL;DR

This paper proposes h3DEB, a novel qutrit-based quantum key distribution protocol that enhances noise resistance by leveraging the hCHSH-3 Bell inequality, which achieves a higher quantum violation factor (v ≈ 1.693) than the CHSH-3 inequality used in the 3DEB protocol. By using tritter-based measurements to implement non-local product observables, the protocol enables secure key distribution with a noise threshold of F ≈ 0.409, surpassing the 3DEB protocol’s threshold of F ≈ 0.304.

ABSTRACT

The Ekert quantum key distribution protocol uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping. The 3DEB protocol uses instead pairs of entangled qutrits to achieve better noise resistance than the Ekert protocol. It performs checks based on a Bell inequality for qutrits named CHSH-3. In this paper, we present a new protocol, which also uses pairs of entangled qutrits, but achieves even better noise resistance than 3DEB. This gain of performance is obtained by using another inequality called here hCHSH-3. As the hCHSH3 inequality involve products of observables which become incompatible when using quantum states, we show how the parties running the protocol can measure the violation of hCHSH3 in the presence of noise, to ensure the secrecy of the key.

Motivation & Objective

• To improve the noise resistance of entanglement-based quantum key distribution protocols using higher-dimensional quantum systems.
• To address the limitation of existing qutrit protocols like 3DEB, which rely on the CHSH-3 Bell inequality with a relatively low violation factor.
• To enable practical implementation of non-local product observables required by the hCHSH-3 inequality using modified tritter configurations.
• To demonstrate that the hCHSH-3 inequality supports a higher quantum violation factor than CHSH-3, leading to better tolerance against channel noise.

Proposed method

• The protocol uses entangled GHZ states of two qutrits to generate correlated measurement outcomes for key generation.
• It employs the hCHSH-3 Bell inequality, a homogeneous inequality with a higher quantum violation factor (v ≈ 1.693) than CHSH-3 (v ≈ 1.436).
• Measurement bases are implemented using tritters parameterized by phase shifts, with specific configurations enabling the implementation of product observables like A_i A_j.
• A key innovation is the use of a modified measurement basis Z† = diag(1, ω², ω) to replace Z, allowing physical realization of non-local product observables via detector permutation.
• The protocol distinguishes between key-generation rounds (labeled 'k') and eavesdropping-check rounds (labeled 'c_i'), using specific pairs of measurement settings to test the hCHSH-3 inequality.
• Noise resistance is quantified by computing the threshold F = 1 - 1/v, where v is the quantum violation factor of the chosen Bell inequality.

Experimental results

Research questions

• RQ1 Can the hCHSH-3 Bell inequality be practically implemented in a quantum key distribution protocol using qutrits?
• RQ2 Does the use of hCHSH-3, with a higher quantum violation factor, lead to improved noise tolerance compared to CHSH-3 in entanglement-based QKD?
• RQ3 How can non-local product observables required by hCHSH-3 be physically realized in a quantum optical setup?
• RQ4 What is the maximum noise threshold F achievable by a qutrit-based QKD protocol using the hCHSH-3 inequality and GHZ states?

Key findings

• The h3DEB protocol achieves a noise resistance threshold of F ≈ 0.409, significantly higher than the 3DEB protocol’s F ≈ 0.304.
• The hCHSH-3 Bell inequality enables a quantum violation factor of v ≈ 1.693 with the GHZ state, exceeding the CHSH-3 violation factor of v ≈ 1.436.
• The protocol successfully implements non-local product observables using modified tritter configurations, overcoming the incompatibility issue of product measurements in quantum mechanics.
• The use of detector permutation to implement Z† instead of Z allows physical realization of the required product observables without additional hardware complexity.
• The protocol maintains security by using specific measurement pairs for eavesdropping detection while preserving key generation in other settings.