Cryptography Reference
In-Depth Information
switch
switch
variable coupler
variable coupler
Figure 2.3
Setup used to prepare and analyze time-bin qubit states.
one of two detectors,
D
0
or
D
1
. Upon tuning the coupling and the phase shift
of the right interferometer of Figure 2.3, we thus can perform any simple qubit
measurement.
We now turn to the issue of generalizing the above scheme and consider
qudits, that is,
d
-dimensional quantum systems. In the context of quantum
information processing, these higher-dimensional systems are interesting to
consider: in quantum key distribution, for example, such systems carry in-
trinsically more information than qubits and are more resilient to noise [12].
Another example is nonlocality tests: it has been possible to construct Bell
inequalities for qudits for which the required detector efficiencies are signifi-
cantly lower than for qubits [13].
It is trivial to extend the two schemes we have described to the case of
qudits. One just adds as many arms to the interferometer as the dimension
of the system one wants to prepare. Again, a variable coupler distributes the
impinging one-photon state among the
d
arms, with a weight amplitude
c
j
for the
j
th arm, resulting in a state that is a superposition of states with one
photon in each arm. The path length difference between any two arms is
much larger than the pulse spread. On each arm
j
, a phase shift
φ
j
is applied.
Finally, a switch is used to direct the
d
parts of this state onto the same fiber.
The state we get reads
j
1
c
j
e
i
φ
j
denotes a state of one photon
lying in the time-bin
j
. First results along the above lines can be found in [14-
16]. Note that all projective Von Neumann measurements can, in principle,
be implemented using this approach.
Let us now see how entangled states can be produced using a nonlinear
crystal in which spontaneous parametric down conversion (SPDC) occurs. In
SPDC, the impinging photon, called the pump photon, is (probabilistically)
converted into two photons called signal and idler. Thus if the pump photon
is in a superposition state of two time-bins (Equation (2.1)), the two-photon
state emerging from the crystal will be
|
j
, where
|
j
=
cos
2
|
e
i
φ
sin
2
|
|
=
0
,
0
+
1
,
1
,
(2.2)
