Cryptography Reference
In-Depth Information
field, so that the polarization setup has perfect spatial overlap and a stable
relative phase by default without active control.
If in the experiment one of the
S
j
components, e.g., the
S
1
component,
is chosen to be large, the quantum Stokes variables effectively acquire the
properties of quadrature operators. The arguments used in the section de-
voted to postselection of coherent states can then be easily extended to the
use of coherent polarization states. The choice of “classical”
S
1
,
S
1
|
1,
corresponds to an almost completely horizontally polarized light beam with
S
2
and
S
3
as noncommuting observables. The
S
2
and
S
3
measurement bases
play the role of two nonorthogonal bases in the BB84 protocol. The
S
2
and
S
3
components can be measured by applying appropriate phase shifts between
a
x
and
a
y
and using a balanced photodetector (see Figure 5.2) [30]. As seen in
Figure 5.2, the switching between these two bases requires the least modifica-
tion in the measurement setup, which is our motivation to use this particular
polarization setting.
Polarization encoding is illustrated in Figure 5.3. A quantum state of
a polarized light can be conveniently represented on the Poincare sphere
[30]. The quantum state of a
p
-polarized light is represented with a quantum
|
S
2
S
3
S
1
Figure 5.3
Polarization encoding of a coherent
p
-polarized state on the Poincare
sphere. The modulation in
S
2
is illustrated for two different modulation amplitudes
(
+
δ
1
S
2
,
+
δ
2
S
2
).