Aspects of entangled translucent eavesdropping in quantum cryptography

Howard E. Brandt
U.S. Army Research Laboratory, 2800 Powder Mill Road, Adelphi, Maryland 20783

John M. Myers
Gordon McKay Laboratory, Harvard University, Cambridge, Massachusetts 02138

Samuel J. Lomonaco, Jr.
Department of Computer Science, University of Maryland, Baltimore County, Maryland 21228

Published in Phys. Rev. A, Vol. 56, No. 6, December 1997, pp. 4456 - 4465.

      We present a mathematical physics analysis of entangled translucent eavesdropping in quantum cryptography, based on the recent work of Ekert, Huttner, Palma, and Peres [Phys. Rev. A 50, 1047 (1994)]. The key generation procedure involves the transmission, interception, and reception of two nonorthogonal photon polarization states. At the receiving end, a positive operator valued measure (POVM) is employed in the measurement process. The eavesdropping involves an information-maximizing von Neumann-type projective measurement. We propose a design for a receiver that is an all-optical realization of the POVM, using a Wollaston prism, a mirror, two beam splitters, a polarization rotator, and three photodetectors. We present a quantitative analysis of the receiver. We obtain closed-form algebraic expressions for the error rates and mutual information, expressed in terms of the POVM-receiver error rate and the angle between the carrier polarization states. We also prove a significant result, namely, that in the entangled translucent eavesdropping approach, the unsafe error rate based on standard mutual information comparisons is equivalent to the maximum allowable error rate based on perfect mutual information for the eavesdropper. In this case, the above unsafe error rate is in fact not overly conservative.