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arXiv:1504.08161

A Quantum Key Distribution Protocol for qudits with better noise resistance

Zoé Amblard, François Arnault

Published Apr 30, 2015• 3 citations
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Abstract

The Ekert quantum key distribution protocol uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping. The N-DEB protocol uses instead pairs of entangled qudits to achieve better noise resistance than the Ekert protocol. It performs checks based on the Bell CGLMP inequality for qudits. In this paper, we present the generalization for qudits of our protocol h3DEB (for qutrits). This protocol also uses pairs of entangled qudits, but achieves even better noise resistance than N-DEB and is showed to be secure against the same family of cloning attacks than N-DEB. This gain of performance is obtained by using another inequality called here hCHSH-$d$. For each party, the hCHSH-$d$ inequality involves $2d$ observables. We explain how the parties can measure these observables and thus are able to check the violation of hCHSH-$d$. In the presence of noise, this violation allows the parties to ensure the secrecy of the key because it guarantees the absence of a local Trojan horse attack. The advantage of our proposed scheme is that it results in an increased resistance to noise while remaining secure against individual attacks.

DOI
10.48550/arxiv.1504.08161

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The Ekert quantum key distribution protocol uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping. The N-DEB protocol uses instead pairs of entangled qudits to achieve better noise resistance than the Ekert protocol. It performs checks based on the Bell CGLMP inequality for qudits. In this paper, we present the generalization for qudits of our protocol h3DEB (for qutrits). This protocol also uses pairs of entangled qudits, but achieves even better noise resistance than N-DEB and is showed to be secure against the same family of cloning attacks than N-DEB. This gain of performance is obtained by using another inequality called here hCHSH-ddd. For each party, the hCHSH-ddd inequality involves 2d2d2d observables. We explain how the parties can measure these observables and thus are able to check the violation of hCHSH-ddd. In the presence of noise, this violation allows the parties to ensure the secrecy of the key because it guarantees the absence of a local Trojan horse attack. The advantage of our proposed scheme is that it results in an increased resistance to noise while remaining secure against individual attacks.
The Ekert quantum key distribution protocol [1] uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping. The 3DEB protocol [2] 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 and found in [3, 4]. In this paper, we present a new protocol, which also uses pairs of entangled qutrits, but gaining advantage of a Bell inequality which achieves better noise resistance than the one used in 3DEB. The latter inequality is called here hCHSH-3 and was discovered in [5]. For each party, the hCHSH-3 inequality involves four observables already used in CHSH-3 but also two products of observables which do not commute. We explain how the parties can measure the observables corresponding to these products and thus are able to check the violation of hCHSH-3. In the presence of noise, this violation guarantees the security against a local Trojan horse attack. We also designed a version of our protocol which is secure against individual attacks.
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.
We consider a generalization of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by NNN- or ddd-dimensional systems (qudits). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerf's formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of qudit generalizations of the Ekert's protocol for qubits.
The study of quantum cryptography and quantum entanglement have traditionally been based on two-level quantum systems (qubits). In this paper, we consider a generalization of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by three-level systems (qutrits). In order to investigate the security against the optimal individual attack, we derive the information gained by a potential eavesdropper applying a cloning-based attack. We exhibit the explicit form of this cloner, which is distinct from the previously known cloners, and conclude that the protocol is more robust than those based on entangled qubits as well as unentangled qutrits.
We propose an extension of quantum key distribution based on encoding the key into quNits, i.e. quantum states in an N -dimensional Hilbert space. In our protocol, we adopt asymmetric measurement scheme resulting in an efficiency higher than previous protocols and a generalized Bell inequality [Phys. Rev. Lett. 92 (2004) 130404] is employed to detect the presence of an eavesdropper Eve. We also derive the information gained by a potential eavesdropper Eve applying a cloning-based attack and the maximal error rate which measures the robustness of the protocol. The result shows that the security of our scheme increases with the dimension N .