Cryptography Reference
In-Depth Information
Figure 2.1
First quantum cryptography experiment outside the lab, in 1995, at the
Swisscom telecommunication center. (From A. Muller et al.,
Europhys. Lett.
33(5), 335-
339, 1996.)
Let us emphasize that more specific reviews exist, for instance and among
others, on time-bit qubits and related experiments in [6], on quantum cryp-
tography in [7], on quantum cryptography and entanglement in [8], and on
Bell inequalities and useful entanglement in [9].
2.2 Time-Bin Qubits and Higher
Dimensions
The fundamental constituent underlying most quantum communication pro-
tocols is the qubit. As a quantum analogue of a classical bit, a qubit is simply a
two-level quantum system. The quantum information carried by a qubit is its
state, which is, according to quantum mechanics, described by a normalized
vector in C
2
.Ifwelet
denote an orthonormal basis of C
2
, the state of
{|
0
,
|
1
}
|
+
|
a qubit reads
a
0
. Also, quantum mechanics prescribes that vectors
that are identical up to a global phase factor essentially describe the same
state. Thus the general state of a qubit can be written as
0
a
1
1
cos
2
|
sin
2
e
i
φ
|
|
ψ
=
0
+
1
,
(2.1)
where
]. A nice feature of this parametrization is that
it allows us to represent conveniently all (pure) qubit states on the surface of a
φ
∈
[0 : 2
π
], and
θ
∈
[0 :
π
