IEEE - Aerospace and Electronic Systems - March 2021 - 39

Amer et al.

Figure 4.
Figure 3.
Showing how measurements may be performed in a polarization
based encoding scheme. A polarized beam splitter (PBS) allows a
qubit to pass one arm only if it is polarized horizontally (denoted
here as a state j0i) or the other arm if it is polarized vertically
(denoted j1i). SPC's can detect the presence of a photon. If jpi ,
the input, is in state j0i , it will always be detected by SPC1. On
the other hand, if jpi ¼ jþi , then either SPC1 or SPC2 will detect
the photon (with 50/50 probability), but not both (abstractly, this
is implementing a Z basis measurement of an X basis state). This
same circuit can be used to implement an X basis measurement
through the use of a half wave-plate (HWP) which rotates the
polarization of the incoming qubit by 45 (thus converting a jþi
to a j0i and a jÀi to a j1i).

modulators, to vary the polarization of a photon emitted
by a single laser (see [66]-[68] for some experimental
implementations using this form of state preparation).
Measurements in a polarization encoding scheme may
also be done through passive or active means. Normally,
both systems consist of passing the photon through a
polarized beamsplitter (PBS) causing any photon horizontally polarized to pass through one output mode while any
photon polarized vertically will output through the other.
At the end of each output, a single photon counter (SPC)
is placed which will " click " if it is hit by a photon (as there
are two outputs to the polarizing beamsplitter, two SPC's
are needed). To measure in the X basis, one may simply
place a half-wave-plate to rotate the polarization 45 and
then repeat the above (or use electrooptic modulators).
See Figure 3. Passive optics may be used to make basis
measurement choices via the use of a beamsplitter
whereas active systems may employ electrooptic modulators before passing through the PBS circuit. For more
information on recent experiments in polarization encoding, and the actual apparatus used, the reader is referred
to [62], [63], [65]-[71].
Phase encoding: Phase-coding [72], [73] is based on
the use of Mach-Zehnder interferometers [74]. A prepares
a single qubit and passes it through the interferometer.
The photon passes the first beamsplitter causing it to travel
in a superposition down both arm a and arm b; the interferomter must be unbalanced so that one arm, say a is longer
than the other to avoid interference at the second beamsplitter. Along arm a, the phase is modulated. The signal is
recombined at the second beamsplitter. The receiver is
similar, though the phase chosen is independent of A's
choice. When both A and B set their phase modulators so
that the difference in shift is either 0 or 180 , the output of
the beamsplitter on the receiving end will be deterministic.
MARCH 2021

Potential implementation of a phase-encoded QKD system with
Alice on the left and Bob on the right. Each party uses an unbalanced interferomter where one arm of the input beamsplitter (BS)
is longer than the other. If both parties choose their phases (f for
A and f0 for B) so that the difference is 0 or 180 , the output of
the second interferometer is deterministic; otherwise it is random.

Otherwise, the photon, on leaving the second beamsplitter
in the receiver's apparatus will randomly hit either photon
counter 0 or photon counter 1. See Figure 4. An interesting
use of unbalanced interferometers in the use of QKD
design is the so-called " plug-and-play " system, also used
commercially [75].
Time-bin encoding: Another popular method of physically realizing a qubit on a photon is through time-bin
encoding [76]; this also has the added benefit of being
able to reliably create high-dimensional quantum
states [18], [19], [77], [78] which can be used in protocols
to achieve higher noise tolerance than similar qubit-based
protocols achieve. Here, typically, a single photon is
passed through an unbalanced interferometer. That is, a
single photon is passed through a beamsplitter, causing it
to travel in a superposition down both a short arm (a) and
a long arm (b). Since one arm is longer, traveling down
this path requires additional time. The signals are recombined at a second beamsplitter. However, since the photon
has not yet been observed, it is now in a superposition of
time slots-traveling in a superposition of the form
p1ﬃﬃ jt0 i þ p1ﬃﬃ jt1 i . Furthermore, the relative phase along an
2
2
arm may be altered, causing the creation of any qubit state
of the form
1
eif
pﬃﬃﬃ jt0 i þ pﬃﬃﬃ jt1 i
2
2

(4)

for user-controlled f. Measuring in the " time basis " jt0 i ,
jt1 i may be done simply by recording the time of detection. Measuring in alternative bases (needed for QKD
security) may be done by passing the photon through a
second interferometer [18].

QUANTUM COMMUNICATION OVER FIBER: DECOY
STATE EFFICIENCY
Regardless of the source and encoding method, two general mediums for quantum communication are available:
fiber and freespace. Fiber involves the transmission of
quantum information, encoded using photons in one of the

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