Optimal Eavesdropping in Quantum Cryptography. I

TL;DR

This paper analyzes the maximum information an eavesdropper can gain in quantum cryptography using the BB84 protocol, deriving bounds and describing an optimal attack strategy involving two qubits.

Contribution

It provides the first explicit derivation of an optimal eavesdropping probe for BB84, including the interaction and measurement process, and relates it to Bell inequality violations.

Findings

Derived an upper bound on accessible information for a given error rate.

Constructed an optimal eavesdropping probe with two qubits that attains the bounds.

Connected quantum cryptography security to Bell's inequalities.

Abstract

We consider the Bennett-Brassard cryptographic scheme, which uses two conjugate quantum bases. An eavesdropper who attempts to obtain information on qubits sent in one of the bases causes a disturbance to qubits sent in the other basis. We derive an upper bound to the accessible information in one basis, for a given error rate in the conjugate basis. Independently fixing the error rate in the conjugate bases, we show that both bounds can be attained simultaneously by an optimal eavesdropping probe, consisting of two qubits. The qubits' interaction and their subsequent measurement are described explicitly. These results are combined to give an expression for the optimal information an eavesdropper can obtain for a given average disturbance when her interaction and measurements are performed signal by signal. Finally, the relation between quantum cryptography and violations of Bell's inequalities is discussed.