Influence of the experimental parameters of the optical fiber in the Quantum Key Distribution, the protocol BB84
In this work, we represent the principle of quantum cryptography (QC) that is based on fundamental laws of quantum physics. QC or Quantum Key Distribution (QKD) uses various protocols to exchange a secret key between two communicating parties. This research paper focuses on and examines the quantum...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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| citation_txt | Influence of the experimental parameters of the optical fiber in the Quantum Key Distribution, the protocol BB84 / L. Bouchoucha, S. Berrah, M. Sellami // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2018. — Т. 21, № 1. — С. 73-79. — Бібліогр.: 12 назв. — англ. |
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| description | In this work, we represent the principle of quantum cryptography (QC) that is based on fundamental laws of quantum physics. QC or Quantum Key Distribution (QKD) uses various protocols to exchange a secret key between two communicating parties. This research paper focuses on and examines the quantum key distribution by using the protocol BB84 in the case of encoding on the single-photon polarization, and shows the influence of optical components' parameters on the quantum key distribution. We also introduce Quantum Bit Error Rate (QBER) to better interpret our results and show its relationship with the intrusion of the eavesdropper, called Eve, on the optical channel to exploit these vulnerabilities.
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2018. V. 21, N 1. P. 73-79.
© 2018, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
73
Optoelectronics and optoelectronic devices
Influence of experimental parameters inherent to optical fibers on
Quantum Key Distribution, the protocol BB84
L. Bouchoucha
1
, S. Berrah
1
, M. Sellami
2
1
Department of Electrical Engineering, LMER laboratory, Faculty of Technology
Abd Rahman MIRA University of Bejaia, Algeria
E-mail: bouchouchalydia.bl@gmail.com, Sm.berrah@gmail.com
2
Center university of Tamnrasset, Algeria
E-mail: sellami_mohammed@yahoo.fr
Abstract. In this work, we represent the principle of quantum cryptography (QC) that is
based on fundamental laws of quantum physics. QC or Quantum Key Distribution (QKD)
uses various protocols to exchange a secret key between two communicating parties. This
research paper focuses and examines the quantum key distribution by using the protocol
BB84 in the case of encoding on the single-photon polarization and shows the influence of
optical components parameters on the quantum key distribution. We also introduce
Quantum Bit Error Rate (QBER) to better interpret our results and show its relationship
with the intrusion of the eavesdropper called Eve on the optical channel to exploit these
vulnerabilities.
Keywords: cryptography, quantum key distribution, BB84 protocol, Qbit, quantum bit
error rate.
doi: https://doi.org/10.15407/spqeo21.01.073
PACS
Manuscript received 04.01.18; revised version received 22.02.18; accepted for publication
29.03.18; published online 29.03.18.
1. Introduction
Quantum cryptography is a solution to the weaknesses
and flaws of classical cryptography that is based on
digital signature, the electronic certificate and the
classical cryptographic protocols (DES, RSA ...) [1] in
the security of the secret key exchanged between two
communicating parties.
Quantum Cryptography called Quantum Key Distri-
bution (QKD) [1-3] converges to use the fundamental
laws of quantum physics to guarantee the security of the
exchanged key [2]. The QKD allows Alice and Bob to
exchange a key by using two communication channels:
the first is the quantum channel that can be the optical
fiber or free space, and the second is the classical channel
that is the public channel that can be Internet or a
telephone line [2-4].
In the view of quantum cryptography, there are two
types of Quantum Key Distribution, the first type is
“prepare and measure” [2]. The protocol BB84 was
published by Bennett and Brassard, it is the first protocol
that has been operating in the first type of QKD, where
Alice sends photons in four possible states by using two
different polarization bases [5]. Then, there was an
improvement of this protocol through polarization of
photons in two non-orthogonal states using the protocol
B92 [2, 6, 7]. Security of single photon with this protocol
was proved by Tamaki et al. [8]. Then, another protocol
was proposed by Pasquinucci and Gisin, which consists in
adding another polarization base forming a protocol with
six polarization states [5, 8-10]. The second type
constituted a new approach of QKD by using quantum
teleportation that is based on the quantum entanglement
(calibration), when Ekret proposed the first protocol based
on Bell’s theorem, called the protocol E91 [2, 5, 11].
In our study, we focus on the first type of QKD,
specifically BB84 protocol in the case of coding on the
single-photon polarization [2, 12]. This distribution is
influenced by intrusion of malicious hackers who exploit
any loopholes that would allow them to be undetectable
and unnoticed by Alice and Bob. These flaws are related
to the influence of physical parameters of optical
components that can be the optical channel (the optical
fiber), single-photon source or photodetectors. The
quantum bit error rate (QBER) is influenced by these
parameters, that’s why it will be the main landmark to
interpret our results; it is that adds to its influence on
mutual information between communicating parties.
SPQEO, 2018. V. 21, N 1. P. 73-79.
L. Bouchoucha, S. Berrah, M. Sellami. Influence of experimental parameters inherent to optical fibers on Quantum …
74
Fig. 1. Quantum cryptography communication.
2. BB84 protocol
The first quantum key distribution protocol was
elaborated by Bennett and Brassard [6], when a secret
key was exchanged between two users Alice and Bob by
using a quantum channel (the optical fiber or free space)
and a classical channel, it is presented in Fig. 1.
The fundamental concept of this protocol is that
Alice randomly selects a series of Qbits, then she sends
them into a quantum channel in the form of photon to
Bob in order to create a secret key. It will be encoding
either on its polarization or phase [1, 3].
In the case of encoding on the polarization of single
photon, BB84 protocol uses two polarization bases: the
linear base and the diagonal one [2-4], to represent the
four polarization states.
Fig. 2 shows that Qbit |0> is represented in the
linear basis by a horizontal polarization state (0°) and in a
diagonal basis – by a diagonal polarization (45°), but the
Qbit |1> is represented in the linear basis by the
horizontal polarization state (90°) and in a diagonal basis
– by an anti-diagonal polarization. i.e. (135°).
The procedure of BB84 protocol is done according
to the following steps [3, 4, 6]: the first step, Alice sends
single photons into the optical channel according to the
four polarization states. Using randomly two polarizers,
the first polarizer allows representation of the vertical
state (90°) or horizontal state (0°) on the linear base, and
the second polarizer allows representing the diagonal
state (45°) or anti-diagonal state (135°) on the diagonal
basis. At the reception, Bob has two analyzers. These
randomly select the base on which they will measure the
state of photon received with 50% probability of
choosing the right polarization.
The second step, after having exchanged photons
constituting the sequence of Qbits sent by Alice. Bob has
to sacrifice a large number of photons received by
sending the bases chosen for measurements of
polarization states on the public channel in order to
compare with those chosen by Alice. The latter
announces the results of comparison in three posts: no
correspondence between bases, 50% correspondence,
correspondence with the personal key [2].
In the third step, if there is a correspondence
between the bases chosen between Alice and Bob; and
there is not the intrusion of an eavesdropper Eve. So, they
randomly select the secret key to share between them and
send it on the public channel. BB84 protocol allows
sharing a series of strongly correlated Qbits constituting
the secret key [3]. In this case, it is checked if the
distribution system is technologically perfect
(components without loss) the keys of Alice and Bob are
identical in the absence of any intervention of Eve.
A. The protocol BB84 without the presence of an
eavesdropper
Ideally, BB84 protocol is perfectly secure [4], its
implementation in practice is not easy because there are
some effects of attenuation and noise in the quantum
channel. In the case of the optical fiber, there are
attenuation of the channel due to the Rayleigh effect, the
effect of the dark count due to the photodetector and the
single photon source. The noise and attenuation reduce
the channel efficiency, and they affect the transmission
distance and the rate of exchange photons.
1) The influence of the source
BB84 protocol requires the use of single photon sources
[3, 4, 12] that allow for an optical pulse comprising
single photon. It is for this fact use of laser sources
strongly attenuated and obeys the Poisson distribution
(µ = 0.1) [14]:
( )
!
,
n
e
np
n µ−
⋅µ
=µ , (1)
n and µ are a number of photons and a number of
photons per pulse, respectively.
2) The influence of quantum channel
During transmission of photons, the latter are exposed to
different effects, namely: effects of absorption,
diffraction and attenuation per unit length due to the
Rayleigh scattering [15]. These interactions and losses in
the optical channel have a significant and major influence
on the probability to detect photons emitted by Alice and
received by Bob, because they modified their properties
(polarization and phase). The used quantum channel is
the single-mode optical fiber. The losses in this type of
fibers in the case of the 1550 nm telecom window reach
α = 0.22 dB/km [3, 5]. The quantum efficiency of the
fiber may thus be defined as follows:
1010
L
fiber
α
−
=η , (2)
where L is the length of optical fiber.
Fig. 2. Polarization basis of the protocol BB84.
SPQEO, 2018. V. 21, N 1. P. 73-79.
L. Bouchoucha, S. Berrah, M. Sellami. Influence of experimental parameters inherent to optical fibers on Quantum …
75
We deduced that the total transfer efficiency
between Alice and the photodetector is related with the
linear losses in the fiber and those in Bob’s detector.
10
Bob
10
α+α
−
=η
L
total . (3)
3) The influence of photodetector
As the power of detected photon is very even lower
intrinsic to a photodiode (APD) that according to the
counter mode allows detection of single photons. The
major drawback of this type of photodetector is the effect
of dark count, which introduces an error in the detection
system. The probability of having the stroke of darkness
per second is related with the detection time window ∆τ:
τ∆⋅= nPdark . (4)
3. Quantum bit error rate
QBER is defined as the ratio between the number of bit
errors to the total number of bits detected by Bob:
erroneouskey
erroneous
NN
N
QBER
+
= , (5)
detopt QBERQBERQBER += . (6)
QBERopt: It determines the error fraction in donation
polarization or phase of photon committed by detector.
Generally, Popt is lower than 1% [3] and can be easily
realized with any instalation; so the QBERopt may be
neglected.
QBERdet: It depends on the probability of darkness rate
and the probability of photon detection.
It is concluded that there are three factors that
influence on QBER: dark count of the detector, the
length of the transmission fiber and quantum efficiency
of the detector.
So, we have:
dtotal
dark
det
n
QBERQBER
η⋅η⋅µ
τ∆⋅
== . (7)
BB84 protocol with the presence of an eavesdropper
In this part, we are interested in the event when a spy
(called Eve) intercepts the emitted photons in the
quantum channel. Knowing that Eve leads a passive
attack that is of the type to intercept and resend [4].
Eve randomly measures the states of photons
intercepted by the analyzer according to the two bases. If
Eve chooses the same polarization basis as Alice to
measure the state of photon, so she returned it to the
channel on the same basis, and Alice and Bob could not
detect the intrusion of Eve. Then, the Qbit sent by Alice
is received by Bob, but the eavesdropper Eve rubbed off
some information from the key exchange between Alice
and Bob. But if Eve chooses a different basis as Alice, it
could be a 50% probability of choosing the right base.
Then, it returns the photon to Bob according to the base
where it makes its measurement.
At the reception, it measures the state of the photon
randomly with the 50% probability of selecting the same
basis as Alice; otherwise, it receives taint photons; so, the
presence of Eve will be detected. After having sent the
photon series on the quantum channel, Bob sent to Alice
the polarization bases, in which he performed
measurements on the classical channel. Alice, in turn,
consults her given basis in what she recorded the
polarization bases chosen to measure states of the emitted
photons. Then, she meets three criteria as seen in the first
case. Despite the step of reconciliation bases between
Alice and Bob; Eve knows each polarization state used,
so there may be a certain amount of information on the
key exchange. The flow of the algorithm of key
reconciliation was better explained and detailed by Omar
and Anas in [1], where they defined the different phases
of reconciliation from the raw key until the amplification
of confidentiality and collection of the final key.
4. The relationship between the theory of information
and QBER
The mutual information measures the security achieved
between the parties on a system or between Alice and
Bob, Alice and Eve and between Eve and Bob. If Eve is
absent on the channel, we designate the mutual
information between Alice and Bob by IAB. On the other
hand, if Eve is present on the channel, then she cuts the
amount of information that Alice sent. It will be
designated by the mutual information between Alice and
Eve as IAE. According to these equations, the condition of
the central theorem can be applied, which is checked
only if the information quantity exchanged between
Alice and Bob is higher than that Eve has intercepted.
IAB > IAE. (8)
We know that the quantum channel and the
equipment have an error rate, which is expressed by
QBER. The latter also has an influence on the amount of
information exchanged for sharing the secret key. So, we
can express mutual information based on previous QBER
as follows where f is the pulse fraction of photons [3]:
( )
( ) ( ),1log1
log1
2
2
QBERQBER
QBERQBERIAB
−⋅−+
+⋅+=
(9)
+
µ
µ
+
+=
22
2
1
2
4 f
f
QBER
I AE . (10)
From the condition IAB = IAE, we will bring
QBER = 15%. So, according to the central theorem,
communication is a secured and the system can create
a key to a value of a lower QBER < 15%. Beyond this
threshold, communication is not secure, and
reconciliation is abandoned, because Eve intercepts
more information than detained by Bob.
SPQEO, 2018. V. 21, N 1. P. 73-79.
L. Bouchoucha, S. Berrah, M. Sellami. Influence of experimental parameters inherent to optical fibers on Quantum …
76
0 20 40 60 80
0
10
20
30
40
Q
B
E
R
,
%
Length, km
Fig. 3. Evolution of QBER based on variations of the fiber
length within the range 1 up to 80 km.
0.0 0.2 0.4 0.6 0.8 1.0
0
10
20
30
40
Q
B
E
R
,
%
Quantum efficiency
Fig. 4. Evolution of QBER based on variations of the detector
quantum efficiency.
5. Simulation and results
Simulation of BB84 protocol by using Matlab offers the
opportunity to perform a study on the influence of
physical parameters on quantum key distribution and the
impact of the spy on safety with this protocol.
Table represents the values of the physical
parameters of the optical components necessary to
implement this simulation.
Table. The physical parameters used in industry in the case of
telecom window 1550 nm.
Number of photons per pulse (µ) 0.1
Losses in the fiber (dB/km) 0.22
Dark count rate (counts/s) 60
Time window (µs) 2
Detector efficiency (dB) 0.2
Fig. 3 shows the influence of variations of the
optical fiber length on the rate QBER. It is obtained for
variations in the optical fiber length within the range 1 to
80 km for the telecom wavelength 1550 nm, which fiber
possesses the linear losses of 0.22 dB/km.
According to the curve, it is clear that the error rate
increases with increasing the length of the optical fiber,
and quality of the link decreases. Knowing that according
to the central theorem; the maximum threshold for secure
communication is performed to a value of less than 15%
of QBER.
In this case, we note that the safety distance is
achieved for the minimum value of 58 km; beyond this
distance the security is breached. It is known that the
linear losses are also related to changes in the length of
the fiber, which plays an important role in the error rate
on QBER.
As shown in Fig. 4, variations of the quantum
efficiency also have their influence on QBER. It is clear
that QBER decreases with increasing the η parameter,
since quality of the optical connection is improved with
increasing the latter. We also note that the value η = 0.05
ensures secure connection given that QBER is less than
the threshold 15%.
The study carried out in this part confirms that Eve
can exploit loopholes due to physical parameters to
intercept the photons carrying the Qbit and be
undetectable by Alice and Bob.
Fig. 5 shows evolution of mutual information
between Alice and Bob and between Alice and Eve based
on QBER. We find that Eve did not intercept the photons
sent by Alice, and it may chance to deduct the photon
polarization states, if the QBER threshold is less than
15%. According to the central communication theorem, it
0 10 20 30 40
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
I
AB
I
AE
∆I
M
u
tu
a
l
in
fo
rm
a
ti
o
n
QBER, %
Fig. 5. Mutual information as a function of QBER variations.
SPQEO, 2018. V. 21, N 1. P. 73-79.
L. Bouchoucha, S. Berrah, M. Sellami. Influence of experimental parameters inherent to optical fibers on Quantum …
77
0 20 40 60 800
10
20
30
Q
B
E
R
,
%
Length, km
a)
0.0 0.2 0.4 0.6 0.8 1.00
10
20
30
Q
B
E
R
,
%
Quantum efficiency
b)
0 10 20 30-1.0
-0.5
0.0
0.5
1.0
I
AB
I
AE
∆I
M
u
tu
a
l
in
fo
rm
a
ti
o
n
QBER, %
c)
0 10 20 30 40 50 60 70 80-1.0
-0.5
0.0
0.5
1.0
I
AB
I
AE
∆IM
u
tu
a
l
in
fo
rm
a
ti
o
n
Length, km
d)
Fig. 7. (a) Evolution of QBER based on variations of the fiber length within the range 1 up to 80 km. (b) Evolution of QBER based on
variations of the detector quantum efficiency. (c) Mutual information as a function of QBER variations. (d) Mutual information as a
function of length variations. ηBob = 0.02, Pdark = 10
−5
.
0 10 20 30 40 50 60 70 80
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
I
AB
I
AE
∆I
M
u
tu
a
l
in
fo
rm
a
ti
o
n
QBER, %
Fig. 6. Mutual information as a function of length variations.
is secure only if IAB > IAE. So, Alice and Bob are able
to develop a secret key. On the other hand, from the
threshold where QBER is above 15%, Eve will have
more information than Bob has received, and the key
will be abandoned. In this case, there will b e
IAB < IAE.
Visualizing Fig. 6 shows the influence of the optical
fiber length on mutual information. We note that the
distance, for which Eve will be able to capture more
information, is 58 km. That meets the threshold required
by QBER 15%. So, it confirms the results obtained in the
latter section.
Fig. 7 allows us to visualize and monitor QBER
based on variations of the fiber length (Fig. 7a), the
quantum efficiency (Fig. 7b) and mutual information
(Fig. 7c), this by taking the detector efficiency
ηBob = 0.02 and Pdark = 10
−5
(the value of probability of
dark counts) [3]. We established that the safety distance
is superior to that we obtained with our experimental
parameters 66 km. However, the threshold limit by
QBER for quantum efficiency is lower, and it is
approximately 0.035. It is less as compared to the results
achieved by us and affects quality of transmission.
SPQEO, 2018. V. 21, N 1. P. 73-79.
L. Bouchoucha, S. Berrah, M. Sellami. Influence of experimental parameters inherent to optical fibers on Quantum …
78
Fig. 8 allows us to visualize and monitor QBER
based on variations of the fiber length (Fig. 8a), the
quantum efficiency (Fig. 8b) and mutual information
(Fig. 8c) by taking the detector efficiency ηBob = 0.01 and
Pdark = 10
−5
(the value of probability of dark counts) [9].
It shows that the safety limit distance for threshold
QBER = 15% is less than the two previous results.
However, achieving quantum efficiency for this
threshold is 0.07 superior as compared to the results
achieved, and quality of transmission will be improved,
but attenuation and losses due to the optical fiber will
influence transmission of the key.
From these three comparisons, one can find that the
optical fiber length affects the photodetector, and this
reflects on the safety distance, and therefore, on
evolution of QBER.
6. Conclusion
The protocol BB84 is a required solution to quantum key
distribution and remedying the intentional attacks of the
eavesdropper.
This paper focuses on the influence of the physical
parameters of optical components on the key distribution
protocol. If these physical parameters allow Eve to
recover a certain amount of information on the
exchanged key, this is the fault of the protocol. As shown
by the results obtained from simulation, the length of the
optical fiber used and the quantum efficiency of the
photodetector have a great influence on the amount of
information exchanged between the communicating
parties and, thus, on the shared key. It was visualized by
variations of QBER and its influence on these
parameters. Therefore, we fixed the lower QBER
threshold at the level 15%; it allows us to have a secure
communication and exchange of secure key, but the
threshold beyond the exchange will not secure, and the
key will be abandoned.
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Authors and CV
Lydia BOUCHOUCHA: was
born in 1991, she received the
master degrees from University
of Bejaia, in 2015, Algeria,
currently, she is a PhD student
at the University of Bejaia,
Algeria, in the quantum
cryptography subject.
Department of Electrical Engineering
LMER laboratory, Faculty of Technology
University of Bejaia, Algeria
E-mail: bouchouchalydia.bl@gmail.com
Smail BERRAH received his
PhD of Sciences from the
University of Sidi bel Abbes in
2006. He is currently a research
professor in the Electrical
Engineering Department at the
University of Bejaia, Algeria.
His research interests include microelectronics, optical
link telecommunication and security.
Department of Electrical Engineering
LMER laboratory, Faculty of Technology
University of Bejaia, Algeria
E-mail: sm.berrah@gmail.com
Mohammed SELLAMI was
born in 1967, he received his
PhD degrees of Sciences from
the University of Constantine,
Algeria, in 2008 currently. He is
a research professor in the
University Center of
Tamanrasset, Algeria.
His research interests are computing and electrical
engineering.
Center University of Tamnrasset, Algeria
E-mail: sellami_mohammed@yahoo.fr
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| id | nasplib_isofts_kiev_ua-123456789-215142 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-21T13:47:34Z |
| publishDate | 2018 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Bouchoucha, L. Berrah, S. Sellami, M. 2026-03-09T09:45:03Z 2018 Influence of the experimental parameters of the optical fiber in the Quantum Key Distribution, the protocol BB84 / L. Bouchoucha, S. Berrah, M. Sellami // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2018. — Т. 21, № 1. — С. 73-79. — Бібліогр.: 12 назв. — англ. 1560-8034 https://nasplib.isofts.kiev.ua/handle/123456789/215142 https://doi.org/10.15407/spqeo21.01.073 In this work, we represent the principle of quantum cryptography (QC) that is based on fundamental laws of quantum physics. QC or Quantum Key Distribution (QKD) uses various protocols to exchange a secret key between two communicating parties. This research paper focuses on and examines the quantum key distribution by using the protocol BB84 in the case of encoding on the single-photon polarization, and shows the influence of optical components' parameters on the quantum key distribution. We also introduce Quantum Bit Error Rate (QBER) to better interpret our results and show its relationship with the intrusion of the eavesdropper, called Eve, on the optical channel to exploit these vulnerabilities. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Optoelectronics and optoelectronic devices Influence of the experimental parameters of the optical fiber in the Quantum Key Distribution, the protocol BB84 Article published earlier |
| spellingShingle | Influence of the experimental parameters of the optical fiber in the Quantum Key Distribution, the protocol BB84 Bouchoucha, L. Berrah, S. Sellami, M. Optoelectronics and optoelectronic devices |
| title | Influence of the experimental parameters of the optical fiber in the Quantum Key Distribution, the protocol BB84 |
| title_full | Influence of the experimental parameters of the optical fiber in the Quantum Key Distribution, the protocol BB84 |
| title_fullStr | Influence of the experimental parameters of the optical fiber in the Quantum Key Distribution, the protocol BB84 |
| title_full_unstemmed | Influence of the experimental parameters of the optical fiber in the Quantum Key Distribution, the protocol BB84 |
| title_short | Influence of the experimental parameters of the optical fiber in the Quantum Key Distribution, the protocol BB84 |
| title_sort | influence of the experimental parameters of the optical fiber in the quantum key distribution, the protocol bb84 |
| topic | Optoelectronics and optoelectronic devices |
| topic_facet | Optoelectronics and optoelectronic devices |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/215142 |
| work_keys_str_mv | AT bouchouchal influenceoftheexperimentalparametersoftheopticalfiberinthequantumkeydistributiontheprotocolbb84 AT berrahs influenceoftheexperimentalparametersoftheopticalfiberinthequantumkeydistributiontheprotocolbb84 AT sellamim influenceoftheexperimentalparametersoftheopticalfiberinthequantumkeydistributiontheprotocolbb84 |