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Revisiting Optimal Eavesdropping in Quantum Cryptography: Choice of Interaction Is Unique up to Rotation of the Underlying Basis.

Atanu Acharyya, Goutam Paul

Published Oct 23, 2016• 0 citations
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Revisiting optimal eavesdropping in quantum cryptography: Optimal interaction is unique up to rotation of the underlying basis

Atanu Acharyya, Goutam Paul

A general framework of optimal eavesdropping on BB84 protocol was provided by Fuchs et al. [Phys. Rev. A 56, 1163 (1997)]. An upper bound on mutual information was derived, which could be achieved by a specific type of interaction and the corresponding measurement. However, uniqueness of optimal interaction was posed as an unsolved problem there and it has remained open for almost two decades now. In this paper, we solve this open problem and establish the uniqueness of optimal interaction up to rotation. The specific choice of optimal interaction by Fuchs et al. is shown to be a special case of the form derived in our work.

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Optimal Eavesdropping in Quantum Cryptography: Choice of Interaction Is Unique up to a Rotation of the Underlying Basis

Atanu Acharyya

A general framework of optimal eavesdropping on BB84 protocol was provided by Fuchs et al. in 1997. An upper bound on mutual information was derived in their work, which could be achieved by a specific type of interaction and the corresponding measurement. However, uniqueness of an optimal interaction was left as an open problem there. We resolve this problem here and establish the uniqueness. Nevertheless, the description of an optimal interaction changes as the basis of description gets rotated. The specific choice of optimal interaction by Fuchs et al. is shown to be a special case of the form provided in our work.

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Security Against Eavesdropping in Quantum Cryptography

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A general framework of optimal eavesdropping on BB84 protocol was provided by Fuchs et al. [Phys. Rev. A 56, 1163 (1997)]. An upper bound on mutual information was derived, which could be achieved by a specific type of interaction and the corresponding measurement. However, uniqueness of optimal interaction was posed as an unsolved problem there and it has remained open for almost two decades now. In this paper, we solve this open problem and establish the uniqueness of optimal interaction up to rotation. The specific choice of optimal interaction by Fuchs et al. is shown to be a special case of the form derived in our work.
A general framework of optimal eavesdropping on BB84 protocol was provided by Fuchs et al. in 1997. An upper bound on mutual information was derived in their work, which could be achieved by a specific type of interaction and the corresponding measurement. However, uniqueness of an optimal interaction was left as an open problem there. We resolve this problem here and establish the uniqueness. Nevertheless, the description of an optimal interaction changes as the basis of description gets rotated. The specific choice of optimal interaction by Fuchs et al. is shown to be a special case of the form provided in our work.