Quantum Information Processing, Vol. 4, No. 1, February 2005 (© 2005)
Securing QKD Links in the Full Hilbert Space
Deborah J. Jackson
and George M. Hockney
Received July 28, 2004; accepted January 31, 2005
Many quantum key distribution QKD analyses examine the link security in a sub-
set of the full Hilbert space that is available to describe the system. In reality,
information about the photon state can be embedded in correlations between the
polarization space and other dimensions of the full Hilbert space in such a way
that Eve can determine the polarization of a photon without affecting it. This
paper uses the concept of suitability Hockney et al. “Suitability versus Fidelity
for Rating Single Photon Guns” to quantify the available information for Eve to
exploit, and demonstrate how it is possible for Alice and Bob to fool themselves
into thinking they have a highly secure link.
KEY WORDS: Quantum key distribution; polarization state; temporal state;
PACS: 03.67.Dd; 03.67.HK; 42.50.-p.
The earliest treatment of quantum key distribution (QKD)
was a the-
oretical paper that deﬁned a method for distant parties (Alice and Bob)
to agree on a random sequence of key bits through the information
encoded and transferred between the them. This approach relies on polar-
ization encoding of photons and is now well known as the BB84 protocol.
Since then, experimenters have used faint laser sources to demonstrate key
exchanges via polarization bases,
phase encoded qubits,
quency encoded qubits.
Another important trend has been the use
of entangled photon pairs for quantum cryptography. Thus far, experi-
ments exploiting the polarization entangled photons
as well as imple-
mentations taking advantage of energy–time entangled photons
Quantum Computing Technologies, Jet Propulsion Laboratory, California Institute of Tech-
nology, 4800 Oak Grove Drive, Pasadena, California 91109-8099, USA.
To whom correspondence should be addressed. E-mail: Deborah.J.Jackson@jpl.nasa.gov
1570-0755/05/0200-0035/0 © 2005 Springer Science+Business Media, Inc.