Quantum Information Processing, Vol. 5, No. 1, February 2006 (© 2006)
Performance Analysis for Brandt’s Conclusive
Jeffrey H. Shapiro
Received October 10, 2005; accepted November 9, 2005
The Fuchs–Peres–Brandt (FPB) probe realizes the most powerful individual
attack on Bennett-Brassard 1984 quantum key distribution by means of a single
controlled-NOT gate in which Alice’s transmitted qubit becomes the control-qubit
input, Bob’s received qubit is the control-qubit output, and Eve supplies the tar-
get-qubit input and measures the target-qubit output. The FPB probe uses the
minimum-error-probability projective measurement for discriminating between the
target-qubit output states that are perfectly correlated with Bob’s sifted bit value
when that bit is correctly received. This paper analyzes a recently proposed mod-
iﬁcation of the FPB attack in which Eve’s projective measurement is replaced by
a probability operator-valued measurement chosen to unambiguously discriminate
between the same two target-qubit output states.
KEY WORDS: Quantum cryptography; quantum key distribution; quantum
PACS: 03.67.Dd; 03.67.Hk; 03.65.Ta.
In an individual attack on single-photon, polarization-based Bennett–
Brassard 1984 quantum key distribution (BB84 QKD), Eve probes Alice’s
photons one at a time. Fuchs and Peres
described the most general
way in which an individual attack could be performed. Eve supplies a
probe photon and lets it interact with Alice’s photon in a unitary manner.
Eve then sends Alice’s photon to Bob, and performs a probability opera-
tor-valued measurement (POVM) on the probe photon she has retained.
Slutsky et al.
demonstrated that the Fuchs–Peres construct—with the
appropriate choice of probe state, interaction, and measurement—affords
Massachusetts Institute of Technology, Research Laboratory of Electronics, Cambridge, MA
02139, USA. E-mail: email@example.com
1570-0755/06/0200-0011/0 © 2006 Springer Science+Business Media, Inc.