Cryptography Reference
In-Depth Information
, without subtracting background of any kind. The incor-
rect outcomes originate mainly from incomplete suppression of the double
pair emission and imperfections in the PBS operation.
F
ψ
−
=
(
0
.
75
±
0
.
05
)
3.2.4 Higher Dimensional Entanglement
for Quantum Communications
In classical communication protocols it is not unusual to send the informa-
tion encoded not only in 0's and 1's but also in a higher number of levels.
For example, when the information is encoded in phase-modulated electrical
signals, coding two bits per phase change doubles the number of bits per
second. This is called two-level coding. This method is suitable, for example,
for 2400 bps modems (CCITT V.26). Encoding more bits per phase change
increases the number of bits per second but, assuming a constant noise, de-
creases the signal-to-noise ratio (SNR). The right choice of level coding per
physical information carrier is a complicated engineering problem which, be-
sides the speed and the SNR, includes the elaboration of new and efficient
communication protocols for higher level encoding.
As we have already reviewed in previous chapters, quantum communi-
cation and quantum computation protocols usually encode the information
in two-dimensional quantum systems, better known as qubits. Nevertheless,
there are ways of enlarging the available dimension of the quantum informa-
tion carrier. A system that is completely described by
n
different orthogonal
vectors is called a qunit. In the same way as in their classical counterpart, the
use of qunits increases the information rate, but surprisingly enough the sys-
tem is also more resistant to noise. For example, entangled qunits can violate
Bell's inequalities more than their two-dimensional counterpart, protecting
in this way the nonlocal quantum correlations against noise. Also, a quan-
tum cryptography protocol using qunits is usually more secure against noise
than those protocols based on qubits [46,47,48]. On the other hand, there are
a series of protocols in quantum communication that are designed specifi-
cally for being implemented in higher dimensional spaces [49,50,51]. On a
more fundamental level, higher dimensional Hilbert spaces provide novel
counterintuitive examples of the relationship between quantum information
and classical information, which cannot be found in two-dimensional sys-
tems [52,53,54].
Encoding qunits with photons has been experimentally demonstrated
using interferometric techniques such as time-bin schemes [55] and super-
positions of spatial modes [56]. Up to now, the only noninterferometric
technique of encoding qunits in photons is using their orbital angular mo-
mentum or, equivalently, their transversal modes [57,58]. Orbital angular
momentum modes usually contain dark spots that regularly exhibit phase
singularities.
The orbital angular momentum of light has already been used to en-
tangle and to concentrate entanglement of two photons [57,59]. This entan-
glement has also been shown to violate a two particle three-dimensional Bell
