Quantum Information Processing, Vol. 4, No. 5, November 2005 (© 2005)
Unambiguous State Discrimination in Quantum Key
Howard E. Brandt
Received March 8, 2005; accepted August 15, 2005
The quantum circuit and design are presented for an optimized entangling probe
attacking the BB84 Protocol of quantum key distribution (QKD) and yielding
maximum information to the probe. Probe photon polarization states become
optimally entangled with the signal states on their way between the legitimate
transmitter and receiver. Although standard von-Neumann projective measurements
of the probe yield maximum information on the pre-privacy ampliﬁed key, if
instead the probe measurements are performed with a certain positive opera-
tor valued measure (POVM), then the measurement results are unambiguous, at
least some of the time. It follows that the BB84 (Bennett–Brassard 1984) proto-
col of quantum key distribution has a vulnerability similar to the well-known vul-
nerability of the B92 (Bennett 1992) protocol.
KEY WORDS: Quantum cryptography; quantum key distribution; quantum
communication; quantum computer; entanglement.
PACS: 03.67.Dd, 03.67.Hk, 03.65.Ta.
It is generally known that the standard two-state B92 protocol of quantum
is not a good solution for quantum key distribu-
Although the two nonorthogonal photon-polarization states of the
protocol cannot in general be distinguished unambiguously by an eaves-
dropping probe without being disturbed, they can be unambiguously dis-
criminated at least some of the time, at the cost of there occurring some
inconclusive events. However, if the inconclusive rate equals the loss rate
of the legitimate receiver (due to attenuation in the key distribution chan-
nel), and only the unambiguous states are relayed by the probe to the
legitimate receiver, then the probe can obtain complete information on the
U.S. Army Research Laboratory, Adelphi, MD, USA. E-mail: email@example.com
1570-0755/05/1100-0387/0 © 2005 Springer Science+Business Media, Inc.