Cryptography Reference
In-Depth Information
key (whenever the choice of bases enables perfect correlation), or to test a Bell
inequality, or it is discarded.
The security of the Ekert protocol is easy to understand: the action of
the eavesdropper Eve acquiring knowledge about the state of the photon
traveling to Bob can be described as adding probabilistic hidden variables
(hidden in the sense that only the eavesdropper knows about their value).
If she gets full information about all states, i.e., if the whole set of photons
analyzed by Bob can be described by hidden variables, a Bell inequality cannot
be violated anymore. If Eve has only partial knowledge, the violation is less
than maximal, and if no information has leaked out at all, Alice and Bob
observe a maximal violation.
Despite its beauty, the Ekert protocol is not very efficient concerning the
ratio of transmitted bits to the sifted key length. As pointed out in 1992 by
Bennett et al. [34] as well as by Ekert et al. [35], protocols originally devised for
single-photon schemes can also be used for entanglement-based realizations.
This is not surprising if one considers Alice's action as a nonlocal state prepa-
ration for the photon traveling to Bob. Interestingly, it turns out that, if the
perturbation of the quantum channel (the QBER) assuming the BB84 protocol
is such that the Alice-Bob mutual Shannon information equals Eve's maxi-
mum Shannon information, then the Clauser-Horne-Shimony-Holt (CHSH)
Bell inequality [36] cannot be violated any more [37,38]. Although this seems
very natural in this case, it is not clear yet to what extent the connection
between the security of quantum cryptography and the violation of a Bell
inequality can be generalized.
In the following, we will first briefly present a test of Bell inequalities over
a distance of 10 km and then comment on some experimental realizations
of quantum key distribution based on photon-pair correlation. We refer the
reader to Chapter 3 of this topic or a survey of other experiments of quantum
communication with entangled photons.
2.4.2.1 Long-Distance Quantum Correlation
As mentioned before, a requirement for entanglement-based QKD is the gen-
eration and the transmission of entangled two-photon states with a degree of
correlation that enables them to violate the CHSH Bell inequality. The largest
spatial separation to date — a distance of 10 km — has been achieved in tests
that were carried out in our group in 1997 and 1998 [5,39,41] (see Figure 2.8).
Further developments in 2002 and 2003 led to the observation of quantum cor-
relation between analyzers connected with up to 50 km of fiber [42-44], but, in
opposition to the first-mentioned experiments, this was realized with fiber on
a spool. All setups relied on photon pairs at telecommunication wavelengths
(either 1310 nm or 1550 nm) suitable for transmission in standard telecom-
munication optical fibers (for a photo of a compact telecommunication wave-
length photon-pair source see Figure 2.9), and fiber-optical interferometers
equipped with Faraday mirrors to compensate polarization effects.
The first series of experiments [5,39,41] took advantage of energy-time en-
tanglement created by spontaneous parametric down-conversion. This type
