OPTIMAL EAVESDROPPING IN QUANTUM CRYPTOGRAPHY .1. INFORMATION BOUND AND OPTIMAL STRATEGY

We consider the Bennett-Brassard cryptographic scheme, which uses two conjugate quantum bases. An eavesdropper who attempts to obtain inform ation on qubits sent in one of the bases causes a disturbance to qubit s 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 basi s. Independently fixing the error rates in the conjugate bases, we sho w that both bounds can be attained simultaneously by an optimal eavesd ropping probe. The probe interaction and its subsequent measurement ar e described explicitly. These results are combined to give an expressi on for the optimal information an eavesdropper can obtain for a given average disturbance when her interaction and measurements are performe d signal by signal. Finally, the relation between quantum cryptography and violations of Bell's inequalities is discussed.