Cryptography Reference
In-Depth Information
correlation as
N
++
+
N
−−
−
N
+−
−
N
−+
E
(φ
A
,
φ
)
=
,
(3.4)
B
N
++
+
N
−−
+
N
+−
+
N
−+
where
N
is the number of coincidence counts when the polarizer is set to
the angle
φ
A
(“
φ
A
(“
+
”)or
−
”) at Alice and when the polarizer is set to the
φ
B
(“
angle
”) at Bob. The CHSH Bell inequality, which holds for
any local realistic description of the photon pair's polarization states, is then
written as a combination of such polarization correlations for a set of angles;
this inequality is
φ
B
(“
+
”)or
−
(φ
A
,
φ
B
)
+
(φ
A
,
(φ
A
,
φ
B
)
|≤
S
=|
E
(φ
A
,
φ
B
)
−
E
E
φ
B
)
+
E
2
,
(3.5)
and
φ
A
(
B
)
where
S
is the so-called Bell parameter and
represent different
polarization settings for Alice (Bob). For a pure singlet state, q
u
antum me-
chanics predicts a maximal violation of this inequality of
S
φ
A
(
B
)
2
√
2
,
for the set
=
A
,
φ
B
,
φ
{
φ
φ
}={
0
◦
,
45
◦
,
22
.
5
◦
,
67
.
5
◦
}
of angles
.
The experimentally obtained polarization correlations are
E
A
,
B
(
0
◦
,
22
.
5
◦
)
=
−
0
.
509
±
0
.
057,
E
(
0
◦
,
67
.
5
◦
)
=+
0
.
643
±
0
.
042,
E
(
45
◦
,
22
.
5
◦
)
=−
0
.
558
±
0
.
055,
45
◦
,
67
5
◦
)
=−
and
E
(
.
0
.
702
±
0
.
046. Using these results, we calculate
S
EXP
=
2
10, which is a sufficient violation of the Bell inequality by over four
standard deviations. It is also the experimental signature of shared entangled
states between the two receiver stations. This work was the first demonstra-
tion of the distribution of entangled photon pairs over free-space optical links.
A cryptographic system based on our setup would have shown a total raw
key generation rate of a few tens of bits per second and an estimated quantum
bit error rate (QBER) of 8.4%. It is interesting to note that our link attenuation
of 12 dB corresponds to a value that might be achievable with state-of-the-
art space technology when establishing a free-space optical link between an
Earth-based receiver telescope of 100-cm diameter and a satellite-based trans-
mitter telescope of 20-cm diameter orbiting Earth at a distance of 600 km [91].
Typical losses in an actual satellite experiment might vary, depending on the
link optics and on the performance of satellite pointing and tracking [92,93].
In an extended experiment, we could significantly increase the distance
between the stations. We have distributed entangled photons between an
old observatory and a modern office skyscraper in Vienna, that are 7
.
41
±
0
.
8km
apart [88]; see Figure 3.12. The source of the entangled photons is placed at the
observatory. The reason for choosing such a distance is that in a 4
.
5-km link
along the ground, one expects the same level of attenuation from scattering
with airborne particles as in going through the whole atmosphere vertically.
∗
In order to have a reasonable signal at this distance, we have built redesigned
.
∗
The transmission of 800 nm light from the whole vertical atmosphere is about 80%
under good weather conditions [94,93]. The horizontal attenuation coefficient mea-
sured in Vienna was approximately
05 km
−
1
. The horizontal distance with the
same attenuation as the whole atmosphere vertically is
L
α
=
0
.
=−
ln
(
0
.
8
)/α
=
4
.
5 km [82].
