Cryptography Reference
In-Depth Information
put an improved lower bound on the speed of “quantum information,” i.e.,
the speed of the propagation of a hypothetical collapse of the wave function:
analysis in the Geneva (laboratory) reference frame led to 2/3
10
7
c
(
c
: the
speed of light) [50], while observation in the frame of the cosmic microwave
background radiation fixed the bound to 1
×
10
4
c
[91,52]. Second, we started
to investigate entanglement of higher-dimensional systems [14-16].
.
5
·
2.4.2.2 Quantum Key Distribution
Obviously, entanglement-based QKD is more complicated to implement than
faint-pulse based schemes. However, as long as technological limitations like
those on detector performance and the lack of efficient true single-photon
sources remain, it also features advantages.
First, as with single-photon based realizations (see Section 2.4.1),
entanglement-based QKD enables Alice to remove the vacuum component
of the generated pulses sent to Bob. Actually, the entanglement-based case is
even more efficient, since the optical losses in Alice's preparation device also
are now eliminated, as can be seen from Figure 2.7c. In addition, depending
on the position of the source, the probability of detecting a photon at Bob's,
conditioned on detection of its twin at Alice's, can be further increased. This
probability is optimal if the source is located in the middle, resulting in a
minimal quantum-bit error rate.
Second, even if two pairs are created within the same detection window —
hence two photons travel towards Bob within the same pulse — they are
completely independent and do not carry the same qubit, although they are
prepared in states belonging to the same basis [92]. Only the photon forming a
pair with the photon detected at Alice'sisinadefinite quantum state; the other
photon is in a completely mixed state. Therefore, eavesdropping attacks based
on multiphoton pulses do not apply in entanglement-based QKD. However,
multiphoton pulses lead to errors at Bob's, who detects from time to time a
photon that is not correlated to Alice's [53].
The third advantage is directly linked to the one mentioned before: be-
yond the passive state preparation, it is even possible to achieve a passive
choice of bases using a setup similar to the one depicted in Figure 2.7d: no ex-
ternal switch that forces all photons in a pulse to be prepared or measured in
a given basis is required, but each photon independently “chooses” its basis
and bit value. Therefore, no fast random number generator or active change
of basis is required.
Finally, the fact that the possibility of distillation of a secret key is intrin-
sically linked to the possibility of violating the CHSH Bell inequality ensures
that the different states are not distinguishable through other uncontrolled de-
grees of freedom [54]. For instance, assuming a faint-pulse or single-photon
based scheme where all states are generated by a different setup [24], differ-
ences in the wavelength of the photons encoding nonorthogonal states would
enable the eavesdropper to acquire full knowledge about the quantum state
sent without perturbing it: in frequency space, all states would be orthogonal.
