1
Experimental quantum key distribution
at a wavelength of λ~850nm
V. Fernandez, D. Arroyo, M. J. Garcia, P. A. Hiskett, Robert J. Collins, Gerald S. Buller, AB. Orue

Summary— Some basic considerations for the experimental
realisation of a quantum key distribution (QKD) system are
discussed in this paper. Among them are the wavelength of the
photon source and the composition of the transmission channel.
In particular, the advantages and disadvantages of using either
λ ~ 850nm or λ ~ 1300/1550nm for the source’s wavelength are
analysed along with a comparison of the performance of optical
fibre versus free space as the physical medium for the
transmission channel.
Keywords—Quantum key distribution, quantum cryptography,
optical data communications, optical fibre, free space
communications, data encryption.
I. INTRODUCTION
T
he realisation of a quantum computer [1][2] could impose
a threat on public key cryptosystems [3], which currently
protect the distribution of cryptographic keys. One proposed
alternative method to distribute keys in a secure manner is
quantum key distribution (QKD) [4] where the key is
encrypted using quantum properties such as the polarisation or
phase of single photons. QKD systems have technologically
evolved considerably over the past few years. Practical
implementations in both optical fibre and free space have
achieved distances as long as 149 km [5] and 144 km [6],
respectively. However the bit rates obtained for most of these
systems (generally less than Kbits-1) are still far from being
competitive with conventional key exchange rates. In addition,
there are still no quantum encryption algorithms that could be
safely used against a quantum computer attack. Therefore
QKD must be used with the only encryption algorithm that has
been mathematically proven: the one time pad [7]. Since this
algorithm states that the cryptographic key must be as long as
the message to ensure secrecy, we must look at ways to
considerably improve QKD transmission rates to make this
process efficient. Accordingly, some technical considerations
affecting this bit rate are discussed in this paper, such as the
photon source’s wavelength or efficiency and the physical
medium composing the transmission channel. Finally the
Veronica Fernandez, David Arroyo, and Maria Jose Garcia are with the
Instituto de Fisica Aplicada, Consejo Superior de Investigaciones Cientificas,
Serrano 144, 28006 Madrid, Spain e-mail: veronica.fernandez@iec.csic.es.
Amalia B. Orue is with the Área de Cultura Científica, CSIC, Serrano 117,
Madrid, Spain. Phil A. Hiskett is with Selex Galileo, Edinburgh, United
Kingdom. Robert J. Collins and Gerald S. Buller are with Heriot-Watt
University, Edinburgh, United Kingdom.
implementation of a free space QKD system for metropolitan
area applications is described. Such system is currently being
designed by our group with the aim of improving current
transmission rates. For this purpose a GHz-clocked photon
source in conjunction with an optical synchronisation of Alice
and Bob - which imposes no software speed constraints - is
proposed.
II. EXPERIMENTAL REALISATION OF QKD
QKD is the only method that offers a verifiably secure
distribution of cryptographic keys between two or more parties
that wish to communicate in absolute secrecy. This secrecy is
not guaranteed by the conjectured impossibility to reverse
certain mathematical functions, such as RSA encryption, but
by Quantum Mechanical laws; in particular the Heisenberg
Uncertainty Principle and the No Cloning theorem [8]. The
latter forbids making a perfect copy of an unknown quantum
state, and since each bit of the key is encrypted by a single
photon this prevents an eavesdropper to copy it. The
Heisenberg Uncertainty Principle (HUP) states there are pairs
of variables, known as conjugate variables that have
associated quantum observables that do not commute. This
means that the measurement of one necessarily disturbs the
other. QKD uses pairs of these conjugate variables, such as
rectilinear and diagonal bases of polarised light. In the first
QKD proposed protocol, the BB84 [4], Alice (the transmitter)
sends a random binary sequence to Bob (the receiver) encoded
in single photons randomly using four polarisation states:,
(which represent the states 0 and 1 using a rectilinear basis +)
,  (which represent the states 0 and 1 using a diagonal basis
×). When a diagonally polarised state (i.e. diagonal basis) is
measured using a vertical orientated polariser (i.e. a rectilinear
basis) the result is ambiguous, since by the HUP it is
impossible to determine whether the state was initially
polarised vertically or diagonally. Therefore Bob, with no
prior information of the basis set that Alice used, will measure
incorrectly in approximately half of the cases. However in the
next stage of the protocol Alice tells Bob by a public channel
which basis she used to generate each of the photons. Bob
keeps only the photons where he used the same basis than
Alice and discards the rest. Alice and Bob should now share a
sequence of bits. If an eavesdropper (Eve) tries to measure the
states, she will necessarily introduce an error, exactly like Bob
does. However, when Alice and Bob compare their basis,
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Bob’s error is eliminated, since they only keep the photons
which they both used the same basis. Therefore, if after this
process there is still an error in Alice and Bob’s sequence they
must conclude that it was someone else who introduced it. A
quantum channel is used to transmit the quantum states
between Alice and Bob and a classical public channel is
utilized to hold the public discussion where they exchange the
basis set, correct errors and detect the presence of an
eavesdropper. The quantum channel is usually composed of
optical fibre or free space whereas the public channel can be
any insecure standard channel, such as a telephone line.
A. Single photon sources
In order to keep the information attained by an
eavesdropper to the minimum, Alice must send only one
photon per bit. This is achieved using a single photon source,
which generates an individual photon when required. One of
the most promising candidates are quantum dots [9][10],
which are excitons (electron-hole pairs) confined in the three
spatial dimensions. When the excitons are confined to such
small areas their energy levels are quantized. If a single
quantum dot contains more than one exciton, they will be
distributed in energy states according to the Pauli Exclusion
Principle. However, as the electrostatic repulsive force is
strong among them due to the reduced area they are embedded
in, each of them will occupy a different energy level [9].
Therefore when they recombine they will emit at different
wavelengths in such a way that the last exciton to recombine
after an excitation pulse takes place, will have a unique
wavelength. Therefore by spectrally filtering this last
wavelength one can dispose of a continuously generated
stream of single photons. However, although considerable
progress is been achieved in the performance of single photon
sources their efficiency is still far from the desired level. This
is partly due to the complexity of achieving the desired density
of states when fabricating a layer of quantum dots. In addition
the collection of the single photon stream into an optical fibre
is not very efficient. Moreover the temperatures necessary to
achieve single photon emission are usually of only a few
Kelvin, with the associated technological difficulties involved
with this. For all of these reasons QKD systems use a more
practical alternative: attenuated laser pulses, often called weak
coherent pulses (WCP), which follow a Poisson distribution
given by:
P(n,  ) 
n
n!
e 
(1)
where P is the probability of finding n photons in a given laser
pulse attenuated to a mean photon number µ. Since an
attenuated laser follows a Poisson distribution there is always a
nonzero probability of finding more than one photon in a given
pulse and therefore µ has to be set to a value where this
probability is sufficiently low to allow secure QKD. A mean
photon number µ of ~ 0.1 is often considered a good
compromise of security, as less than 0.5% of all emitted laser
pulses contain more than 1 photon. However this also means
that 90% of the laser pulses are empty, considerably reducing
the transmission rate of a QKD system.
B. Advantages of using the first telecommunications window
for the photon source of a QKD system
There are typically three different wavelengths that are
commonly used for the photon source of a QKD system. These
correspond to the first, second and third telecommunication
windows, located around λ ~ 800 nm, λ ~ 1300 nm and
λ ~ 1550 nm wavelengths, respectively.
The advantage of choosing the first window relies mainly in
the possibility of taking advantage of the more mature
technology of Silicon-based single photon detectors. They
generally allow for a more efficient detection of single photons
at shorter wavelengths and they are commercially off-the-shelf
components. This permits the operation at high repetition
rates, which in QKD systems – with the impossibility of using
quantum repeaters to amplify the optical signal due to the No
cloning theorem [8] – means the only possibility of increasing
the key transmission rate.
As for the transmission channel, free space is a good
candidate when using the first telecommunication window as
the wavelength’s source, since a low absorption window is
situated in the proximity of λ ~ 850 nm. However, if optical
fibres are chosen instead, there are two main options. The first
option requires the use of single-mode at λ ~ 850 nm optical
fibres. However these fibres are not standard components,
meaning that they are usually more expensive and not always
compatible with other commonly-used standard optical
components (single mode at λ ~ 1550 nm). Alternatively P. D.
Townsend proposed [11] using standard telecommunication
fibre in conjunction with a λ ~ 850 nm-wavelength source. In
this case, Alice and Bob’s stations would use single mode
components at λ ~ 850 nm and standard telecommunications
fibre for the quantum channel. Of course, standard
telecommunication fibre is not single mode at λ ~ 850 nm, and
in fact there are two linear polarisation modes propagating:
LP01 and LP11 [12] (see Fig.1). However, after mode control
techniques, such as fusion splicing of both single-mode fibres
at λ ~ 850nm and λ ~ 1550nm, only 0.4% of the photons are
launched into the secondary mode LP11 and 99.6% are
launched into the fundamental mode LP01.
However, a wavelength of λ ~ 850nm is characterised by an
attenuation of ~ 2dB/km in a standard optical fibre. This value
is considerably higher than those of λ ~ 1300 nm and
λ ~ 1550 nm wavelengths, which are 0.35 dB/km and 0.2
dB/km, respectively. So why not use these wavelengths instead
of λ ~ 850 nm? The reason for this is the lack of suitably
efficient, single-photon detectors. Previous work has shown
that prime candidates for these detectors are Ge and
InGaAs/InP single-photon avalanche diode detectors. However
they suffer from high dark-count rates, and need to be cooled
down to cryogenic temperatures. In addition they show the
deleterious effects of afterpulsing [13][14] where an avalanche
current can fill mid-gap trap states in the material which emit
carriers that subsequently cause further ‘dark’ avalanches. This
3
effect restricts the repetition rates to typically tens of KHz or a
few MHz. The improvement and development of these
detectors is still being investigated, but the afterpulsing effect
in particular remains dominant.
Fig. 1. Mode profile of 850 nm wavelength when propagating in standard
telecommunication fibre for two cases: a) before mode control and b) after
mode control.
C. GHz-clocked QKD
As mentioned in the previous section the use of the mature
technology of Silicon-based single photon detectors in
conjunction with the first telecommunications window allows
the operation of a QKD system at high clock rates, typically of
GHz, albeit over shorter distances (<20 km) due to a higher
attenuation on standard telecommunications fibre. However
this also constitutes an attractive alternative over systems that
use λ ~ 1550 nm, especially for secure communications at an
urban-distance range, such as for companies situated in the
same city that are linked by short distances and require high
transmission rates. Fig. 2 shows typical bit rates measured at
Bob with fibre-based QKD systems using the wavelengths
under discussion [15][16]. We can see differences of several
orders of magnitude in the transmission rates of both systems.
Fig. 2. Comparison of the bit rates achieved for a QKD system that uses a
wavelength of λ ~ 850nm and silicon SPADs [15] and a system that uses a
wavelength of λ ~ 1550nm and InGaAs SPADs [16].
D. Free space or optical fibre as the transmission medium?
The transmission channel of a QKD system must preserve
the ‘purity’ of the quantum states. However if we consider
optical fibre as the transmission medium there are several
phenomena that take place in this medium which degrade the
polarization states. These phenomena are due to
inhomogeneities associated to any material, either due to its
atomic composition or to imperfections in the fabrication
process. As a consequence, birefringence, polarisation mode
dispersion or polarisation dependent losses are phenomena that
commonly take place and need to be considered in optical
transmission by fibre.
Birefringence has its origin in the presence of two or more
optical axes in a material which causes two different refraction
indexes. These axes are due to either the presence of two
natural atomic distributions in the material or to external
factors such as pressure, temperature, etc. As a consequence an
electromagnetic wave will propagate at two different local
velocities, which are commonly known as fast and slow axes.
This will introduce a phase shift between the components of
the light projected along these two axes which will in turn
cause a variation in its polarisation state. Therefore polarised
light propagating through optical fibre will suffer random
variations in its polarisation state which, if not properly
compensated, will degrade the quantum states and
subsequently cause errors in the transmission.
Moreover birefringence is associated to other phenomena
that can degrade the performance of a QKD system. Some of
them are polarisation mode dispersion and polarisation
dependent loss. Due to the presence of two local velocities
mentioned previously in the optical fibre, a polarised state will
be divided into two orthogonal polarisation modes that will
travel at different velocities causing the original pulse to be
temporally broadened which will cause errors in the
transmission. This ultimately limits the maximum repetition
rate o transmission rate over an optical fibre.
Another common effect that appears as a consequence of
birefringence is polarisation dependent loss. The two
orthogonal polarisation modes are differently absorbed in the
optical fibre causing the relative angle of the states encoding
the binary states of the cryptographic key to differ [17]. Since
the security of the BB84 protocol or B92 protocol relies
heavily on this angle special care must be paid to compensate
for this effect.
Moreover optical fibre considerably absorbs certain nearinfrared and infrared wavelengths, especially the first
telecommunication window, λ ~ 850 nm, which is absorbed at
a rate of 2.2 dB per km.
On the other hand, free space is characterised for being a
low birefringent and dispersive medium, besides offering a
low-absorption window close to λ ~ 770 nm, allowing the use
of the Si-based single photon detectors, which offers a series
of previously mentioned advantages. In addition free-space
communications generally offer more flexibility in terms of
installation and lower cost than optical fibre.
However, the most important advantage that the atmosphere
uniquely offers is the possibility of secure global
communication. Indeed, through the atmosphere two remote
locations could communicate by using a low orbit satellite as
secure relay station. Instead, QKD systems that use optical
fibre are limited by both the absorption and the impossibility
of using quantum repeaters. However it must be noted that
free-space QKD systems have some associated problems such
as weather dependency or the necessity of having an open
channel between sender and receiver. In addition turbulence
4
present in the atmosphere due to variations in the density of
the air can cause fluctuations in the alignment of the laser
beam of these systems which need to be compensated for.
E. Short distance urban-area free space QKD system
Research on free-space QKD systems has been especially
focused on increasing the transmission distance of the secure
free-space links in locations situated far from urban areas.
This is mainly aimed to develop satellite-based secure
communications. However, much less attention has been paid
in short-distance QKD applications in urban areas. This is
probably due to higher contributors to turbulence from
industrial equipment (ducts, pipes), machines (internal
combustion engine) or from vehicles, which affect the laser
beam alignment. In addition the laser light is further attenuated
due to a higher absorption by pollutants (see Fig. 3). Despite
this inconvenience short-range free-space systems offer several
advantages. A satellite can be considered as a third party of a
QKD protocol that needs to be established as a secure relay
station. This is not a trivial task. Additionally long-distance
free-space QKD systems are technologically considerably
more challenging, and due to the higher distances involved the
transmission bit rates are much lower. Therefore many
companies situated in urban areas might find a short-distance
free-space QKD system an alternative option since it can offer
higher bit rate, lower cost and less complexity in the
fabrication than long-distance free-space systems.
Fig. 3. Transmission coefficient T versus wavelength for a horizontal path of
1km for two types of aerosol, calculated using an atmospheric transmission
simulation code (Modtran4.0).
For these reasons we’re building a short-distance QKD
system as that shown in Figs. 4 and 5, capable of transmitting
quantum keys securely between two locations in Madrid
situated at 3 km of distance at high transmission rates. These
two locations will be the Institute of Applied Physics (CSIC)
and the telecommunications operator Telefonica. Alice will
use a fast GHz pre-programmed pulse pattern generator to
produce the cryptographic key that, in conjunction with
commercially available Si single photon detectors (SPCMAQR-12) will allow the transmission rates in the order of
Mbits-1. The pre-programmed pseudorandom sequence will
feed four vertical laser diodes which will generate the four
polarisation states required to implement the BB84 protocols,
respectively. A beam expander will be used to generate a
collimated and sufficiently large beam in order to decrease
divergence effects. At Bob, a cassegrain telescope will be used
to efficiently focus the beam and detect the signal from Alice.
In addition a high speed Time Interval Analyser (TIA) with
four channels will allow us to analyse the optical signal from
Alice and establish the degree of security in the transmission.
Especial care must be paid to one of the most critical parts of
the system, which is the filtering of the solar background
radiation from the sun. For this purpose, a combination of
spatial, spectral and software filtering will be used. The timing
synchronisation between Alice and Bob’s stations will be
performed by multiplexing a different wavelength than that
used for the quantum states encrypting the key. This will
permit faster synchronisation compared to systems using
software phase locked loop driven by either the photo
detection events received at Bob [18] or by the Global
Positioning System (GPS) [6]. This type of synchronisation in
conjunction with a GHz-driven source will result in bit
transmission rates in the order of MBits-1.
To the authors’ knowledge no QKD system has been built
in a city that works at this clock frequency and distance.
Current systems for this application are typically clocked at
only a few MHz [19], and the secure key transmission rates are
in the order of a few Kbits-1 or less.
The authors have previously achieved high key
transmission rates operating at high clock frequencies over
optical fibre in a GHz clocked QKD system [15][17].
Fig. 4. The transmitter’s station: Alice. ES is an electrical splitter, LD is a
laser diode, M1 is a mirror, and D is a photodiode. This example illustrates the
BB84 protocol. The black lines represent electrical cables and the grey ones
optical paths.
Fig. 5. The receiver’s station: Bob. PBS is a polarising beam splitter and D1,
D2, D3 and D4 are single photon detectors.
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III. CONCLUSIONS
In this paper we have discussed some technical
considerations affecting the transmission bit rates of a QKD
system. Among them were the wavelength and transmission
medium, along with the advantages and disadvantages of
current long-range free-space QKD systems. Finally a shortdistance high-speed QKD system has been proposed as an
alternative option to current systems as it offers the possibility
of higher transmission rates and a cheaper and easier-toimplement alternative for urban-span secure communications
links.
ACKNOWLEDGMENT
We would like to thank the Ministerio of Educación y
Ciencia, proyecto TSI2007_62657 and CDTI, Ministerio de
Industria, Turismo y Comercio (Spain), in collaboration with
Telefónica I+D, Project SEGUR@ with reference CENIT-2007
2004.
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Veronica Fernandez received the B.Sc. degree (hons.) in physics with
electronics from the University of Seville, Spain, in 2002 and the PhD degree
in physics from Heriot-Watt University, Edinburgh, U.K., in 2006. She joined
the Scientific Research Council (CSIC), Spain, in 2007. Her areas of research
include quantum key distribution and chaotic cryptography.
David Arroyo received the M.S. degree in telecommunications engineering
from the University of Seville, Spain, in 2002. He is working toward the PhD
degree of in physics of complex systems at the Polytechnic University of
Madrid, Spain, since 2005. He joined the Scientific Research Council (CSIC),
Spain, in 2005. His research interests are in the area of cryptography and
chaotic systems.
Maria-Jose Garcia-Martinez received the Telecommunications Engineering
degree from the Universidad Politécnica de Cartagena (UPCT), Spain, in
2006, and did her graduate thesis while at their Department of Information
Technologies and Communications. She is currently working as a grant
holder in collaboration with the Scientific Research Council (CSIC).
Philip Hiskett received a B.Sc. degree (Hons) in Physics from the University
of Leeds, UK, in 1994; an M.Sc. degree in Optoelectronic and Laser Devices
from Heriot-Watt University, Edinburgh UK in 1996 and a Ph.D. degree in
Physics from Heriot-Watt University in 2000. He has held post-doctoral
positions at Heriot-Watt University, working on time-of-flight ranging, single
photon-counting technologies and quantum key distribution, and at Los
Alamos National Laboratory, USA, working on fibre-optic quantum key
distribution systems. He is currently employed as a Senior Systems Engineer
at Selex Galileo, Edinburgh, UK.
Robert J. Collins received an MPhys. with honors degree (4 years) in physics
from the Heriot-Watt University, Edinburgh, UK, in 2003. In 2004 he started
a PhD in physics at Heriot-Watt University. His areas of research include
quantum key distribution, single-photon sources, random number generation,
equipment interfacing, time-of-flight laser ranging, data analysis and software
development.Robert is a member of the Institute of Physics (UK) and the
Institute of Electrical and Electronics Engineers.
Gerald S. Buller (M’06) received the BSc degree (with honors) in natural
philosophy from the University of Glasgow, Glasgow, UK, in 1986 and the
PhD degree in physics from Heriot-Watt University, Edinburgh, UK, in 1989.
He was made a professor of physics at Heriot-Watt University in October
2006. Since 1990, he has led the Photon-Counting Group in researching timeresolved photoluminescence, time-of-flight ranging and quantum key
distribution. Prof. Buller has coauthored more than 200 journal articles,
conference papers, and patent applications in the areas of photon-counting,
semiconductor optoelectronics, optical coatings, and optical interconnects. In
2002 Prof. Buller founded Helia Photonics Ltd. of Livingston, Scotland. He is
a Fellow of the Institute of Physics (UK) and a member of the Optical Society
of America.
Amalia Beatriz Orue received the Telecommunications Engineering degree
from the Universidad de Oriente, Santiago de Cuba, Cuba (1984) and the
DEA from the UPM en 2007. She joined the Área de Cultura Científica of the
CSIC in 2005. She has been Professor of Circuit Theory at the Universidad de
Oriente (1984/2002) and visiting scientist at the CSIC (1999/2000). Her areas
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of research include cryptography, chaotic systems, circuit theory, knowledge
structure and learning theory.