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arXiv:quant-ph/0308030 · Physical Review A

Experimental eavesdropping attack against Ekert’s protocol based on Wigner’s inequality

Fabio Antonio Bovino, A.M. Colla, Giuseppe Castagnoli, Stefania Castelletto, Ivo Pietro Degiovanni, Maria Luisa Rastello

Published Sep 29, 2003• 2 citations
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Abstract

We experimentally implemented an eavesdropping attack against the Ekert protocol for quantum key distribution based on the Wigner inequality. We demonstrate a serious lack of security of this protocol when the eavesdropper gains total control of the source. In addition we tested a modified Wigner inequality which should guarantee a secure quantum key distribution.

DOI
10.1103/physreva.68.034309

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We experimentally implemented an eavesdropping attack against the Ekert protocol for quantum key distribution based on the Wigner inequality. We demonstrate a serious lack of security of this protocol when the eavesdropper gains total control of the source. In addition we tested a modified Wigner inequality which should guarantee a secure quantum key distribution.
In this paper we prove both theoretically and experimentally the insecurity of the Ekert’s protocol for quantum-key distribution when based on the Wigner inequality when entangled photon pairs are used as source. The security proof of the Eckert’s protocol based on Wigner’s inequality consists in verifying the violation of W ≥ 0 (which corresponds to local-realistic theories). We highlight that a violation of the Wigner’s inequality occurs when Eve controls the two quantum channels. We give the theoretical motivation for this result and we perform an experiment proving this weakness, by realizing the condition of Eve gaining total control of the source of photon pairs. In addition we calculate the modified version of this inequality which guarantees safe quantum-key distribution, thus proving it experimentally.
Violation of modified Wigner inequality in a binary bipartite quantum system allows the discrimination between the quantum world and the classical local-realistic one, and also ensures the security of Ekert-type quantum key distribution protocol. In this paper we study both theoretically and experimentally the bounds of quantum correlation associated to the modified Wigner's inequality finding the optimal experimental configuration for its maximal violation. We also extend this analysis to the implementation of Ekert's protocol.
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 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.