Cryptography Reference
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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 ).
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