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33
Note, in addition, that using many-path interferometers
resentation, which applies to all two-levels quantum sys-
opens up the possibility to code quantum systems of dimen-
tems, can also be used to represent phase-coding states.
sions larger than 2, like qutrits, ququarts, etc. (Bechmann-
In this case, the azimuth angle represents the relative
Pasquinucci and Tittel 2000, Bechmann-Pasquinucci and
phase between the light having propagated along the two
Peres 2000, Bourennane et al. 2001a).
arms. The elevation corresponds to the coupling ratio of


25
be equal within a fraction of the coherence time of the ter (1996 and 2000b), up to distances of 48 km of installed
optical ¬ber 35 .
photons. This implies that the path di¬erences must be
matched within a few millimeters, which does not con-
stitute a problem. Besides, the imbalancement must be
chosen so that it is possible to clearly distinguish the 2. The “Plug-&-Play” systems
three temporal peaks and thus discriminate interfering
from non-interfering events. It must then typically be As discussed in the two previous sections, both polar-
larger than the pulse length and than the timing jitter ization and phase coding require active compensation of
of the photon counting detectors. In practice, the second optical path ¬‚uctuations. A simple approach would be
condition is the most stringent one. Assuming a time to alternate between adjustment periods, where pulses
jitter of the order of 500ps, an imbalancement of at least containing large numbers of photons are exchanged be-
1.5ns keeps the overlap between the peaks low. tween Alice and Bob to adjust the compensating system
The main di¬culty associated with this QC scheme is correcting for slow drifts in phase or polarization, and
that the imbalancements of Alice™s and Bob™s interferom- qubits transmission periods, where the number of pho-
eters must be kept stable within a fraction of the wave- tons is reduced to a quantum level.
length of the photons during a key exchange to maintain An approach invented in 1989 by Martinelli, then at
correct phase relations. This implies that the interfer- CISE Tecnologie Innovative in Milano, allows to auto-
ometers must lie in containers whose temperature is sta- matically and passively compensate all polarization ¬‚uc-
bilized. In addition, for long key exchanges an active tuations in an optical ¬ber (see also Martinelli, 1992).
system is necessary to compensate the drifts34 . Finally, Let us consider ¬rst what happens to the state of po-
in order to ensure the indistinguishability of both inter- larization of a pulse of light travelling through an op-
fering processes, one must make sure that in each inter- tical ¬ber, before being re¬‚ected by a Faraday mirror
ferometer the polarization transformation induced by the “ a mirror with a » Faraday rotator36 “ in front, and
4
short path is the same as the one induced by the long one. coming back. We must ¬rst de¬ne a convenient descrip-
Alice as much as Bob must then use a polarization con- tion of the change in polarization of light re¬‚ected by
troller to ful¬ll this condition. However, the polarization a mirror under perpendicular incidence. Let the mirror
transformation in short optical ¬bers whose temperature be in the x-y plane and z be the optical axis. Clearly,
is kept stable, and which do not experience strains, is all linear polarization states are unchanged by a re¬‚ec-
rather stable. This adjustment does thus not need to be tion. But right-handed circular polarization is changed
repeated frequently. into left-handed and vice-versa. Actually, after a re¬‚ec-
Paul Tapster and John Rarity from DERA working tion the rotation continues in the same sense, but since
with Paul Townsend were the ¬rst ones to test this sys- the propagation direction is reversed, right-handed and
tem over a ¬ber optic spool of 10 kilometers (1993a and left-handed are swapped. The same holds for elliptic po-
1993b). Townsend later improved the interferometer by larization states: the axes of the ellipse are unchanged,
replacing Bob™s input coupler by a polarization splitter
to suppress the lateral non-interfering peaks (1994). In
this case, it is unfortunately again necessary to align the
polarization state of the photons at Bob™s, in addition to 35
Note that in this experiment Hughes and his coworkers
the stabilization of the interferometers imbalancement. used an unusually high mean number of photons per pulse
He later thoroughly investigated key exchange with phase (They used a mean photon number of approximately 0.6 in
coding and improved the transmission distance (Marand the central interference peak, corresponding to a µ ≈ 1.2 in
and Townsend 1995, Townsend 1998b). He also tested the pulses leaving Alice. The latter value is the relevant one
the possibility to multiplex at two di¬erent wavelengths for an eavesdropping analysis, since Eve could use an inter-
a quantum channel with conventional data transmission ferometer “ conceivable with present technology “ where the
over a single optical ¬ber (Townsend 1997a). Richard ¬rst coupler is replaced by an optical switch and which allows
Hughes and his co-workers from Los Alamos National her to exploit all the photons sent by Alice.). In the light of
Laboratory also extensively tested such an interferome- this high µ and of the optical losses (22.8 dB), one may argue
that this implementation was not secure, even when taking
into account only so-called realistic eavesdropping strategies
(see VI I). Finally, it is possible to estimate the results that
other groups would have obtained if they had used a similar
34
Polarization coding requires the optimization of three pa-
value of µ. One then ¬nds that key distribution distances
rameters (three parameters are necessary for unitary polar-
of the same order could have been achieved. This illustrates
ization control). In comparison, phase coding requires opti-
that the distance is a somewhat arbitrary ¬gure of merit for
mization of only one parameter. This is possible because the
a QC system.
coupling ratios of the beamsplitters are ¬xed. Both solutions 36
These components, commercially available, are extremely
would be equivalent if one could limit the polarization evolu-
compact and convenient when using telecommunications
tion to rotations of the elliptic states, without changes in the
wavelengths, which is not true for other wavelengths.
ellipticity.


26
but right and left are exchanged. Accordingly, on the there are N such elements in front of the Faraday mirror,
Poincar´ sphere the polarization transformation upon re-
e the change in polarization during a round trip can be
¬‚ection is described by a symmetry through the equa- expressed as (recall that the operator FTF only changes
torial plane: the north and south hemispheres are ex- the sign of the corresponding Bloch vector m = ψ|σ|ψ ):
changed: m ’ (m1 , m2 , ’m3 ). Or in terms of the qubit
’1 ’1
U1 ...UN F T F UN ...U1 = F T F (39)
state vector:

ψ1 ψ2 The output polarization state is thus orthogonal to the
T: ’ (37)

ψ2 ψ1 input one, regardless of any birefringence in the ¬bers.
This approach can thus correct for time varying birefrin-
This is a simple representation, but some attention has gence changes, provided that they are slow compared to
to be paid. Indeed this transformation is not a unitary the time required for the light to make a round trip (a
one! Actually, the above description switches from a few hundreds of microseconds).
right-handed reference frame XY Z to a left handed one By combining this approach with time-multiplexing
˜ ˜
XY Z, where Z = ’Z. There is nothing wrong in doing in a long path interferometer, it is possible to imple-
so and this explains the non-unitary polarization trans- ment a quantum cryptography system based on phase
formation37 . Note that other descriptions are possible, coding where all optical and mechanical ¬‚uctuations are
but they require to arti¬cially break the XY symmetry. automatically and passively compensated (Muller et al.
The main reason for choosing this particular transforma- 1997). We performed a ¬rst experiment in early 1997
tion is that the description of the polarization evolution (Zbinden et al., 1997), and a key was exchanged over an
in the optical ¬ber before and after the re¬‚ection is then installed optical ¬ber cable of 23 km (the same one as in
straightforward. Indeed, let U = e’iωBσ„“/2 describe this the case of polarization coding mentioned before). This
setup features a high interference contrast (fringe visi-
evolution under the e¬ect of some modal birefringence
bility of 99.8%) and an excellent long term stability and
B in a ¬ber section of length „“ (σ is the vector whose
clearly established the value of the approach for QC. The
components are the Pauli matrices). Then, the evolution
fact that no optical adjustments are necessary earned it
after re¬‚ection is simply described by the inverse opera-
the nickname of “plug & play” set-up. It is interesting to
tor U ’1 = eiωBσ„“/2 . Now that we have a description for
note that the idea of combining time-multiplexing with
the mirror, let us add the Faraday rotator. It produces
Faraday mirrors was ¬rst used to implement an “optical
a π rotation of the Poincar´ sphere around the north-
e
2
microphone” (Br´guet and Gisin, 1995)38 .
e
’iπσz /4
south axis: F = e (see Fig. 17). Because the
However, our ¬rst realization still su¬ered from certain
Faraday e¬ect is non-reciprocal (remember that it is due
optical ine¬ciencies, and has been improved since then.
to a magnetic ¬eld which can be thought of as produced
Similar to the setup tested in 1997, the new system is
by a spiraling electric current), the direction of rotation
based on time multiplexing as well, where the interfering
around the north-south axis is independent of the light
pulses travel along the same optical path, however, in
propagation direction. Accordingly, after re¬‚ection on
di¬erent time ordering. A schematic is shown in Fig. 18.
the mirror, the second passage through the Faraday ro-
Brie¬‚y, to understand the general idea, pulses emitted
tator rotates the polarization in the same direction (see
at Bobs can travel either via the short arm at Bob™s, be
again Fig. 17) and is described by the same operator F .
re¬‚ected at the Faraday mirror FM at Alice™s and ¬nally,
Consequently, the total e¬ect of a Faraday mirror is to
back at Bobs, travel via the long arm. Or, they travel
change any incoming polarization state into its orthogo-
¬rst via the long arm at Bob™s, get re¬‚ected at Alice™s,
nal state m ’ ’m. This is best seen on Fig. 17, but can
travel via the short arm at Bob™s and then superpose
also be expressed mathematically:
with the ¬rst mentioned possibility on beamsplitter C1 .
We now explain the realization of this scheme more in

ψ1 ψ2
FTF : ’ (38) detail: A short and bright laser pulse is injected in the

ψ2 ’ψ1
system through a circulator. It splits at a coupler. One
of the half pulses, labeled P1 , propagates through the
Finally, the whole optical ¬ber can be modelled as con-
short arm of Bob™s set-up directly to a polarizing beam-
sisting of a discrete number of birefringent elements. If
splitter. The polarization transformation in this arm is
set so that it is fully transmitted. P1 is then sent onto
the ¬ber optic link. The second half pulse, labeled P2 ,
37
Note that this transformation is positive, but not com-
pletely positive. It is thus closely connected to the partial
transposition map (Peres 1996). If several photons are entan-
38
Note that since then, we have used this interferometer for
gled, then it is crucial to describe all of them in frames with
various other applications: non-linear index of refraction mea-
the same chirality. Actually that this is necessary is the con-
surement in ¬bers (Vinegoni et al., 2000a), optical switch
tent of the Peres-Horodecki entanglement witness (Horodecki
(Vinegoni et al., 2000b).
et al. 1996).


27
takes the long arm to the polarizing beamsplitter. The e¬ective repetition frequency. A storage line half long as
polarization evolution is such that it is re¬‚ected. A phase the transmission line amounts to a reduction of the bit
modulator present in this long arm is left inactive so that rate by a factor of approximately three.
it imparts no phase shift to the outgoing pulse. P2 is Researchers at IBM developed a similar system simul-
also sent onto the link, with a delay of the order of 200 taneously and independently (Bethune and Risk, 2000),
ns. Both half pulses travel to Alice. P1 goes through a also working at 1300 nm. However, they avoided the
coupler. The diverted light is detected with a classical problems associated with Rayleigh backscattering, by re-
detector to provide a timing signal. This detector is also ducing the intensity of the pulses emitted by Bob. As
important in preventing so called Trojan Horse attacks these cannot be used for synchronization purposes any
discussed in section VI K. The non-diverted light prop- longer, they added a classical channel wavelength mul-
agates then through an attenuator and a optical delay tiplexed (1550 nm) in the line, to allow Bob and Alice
line “ consisting simply of an optical ¬ber spool “ whose to synchronize their systems. They tested their set-up
role will be explained later. Finally it passes a phase on a 10 km long optical ¬ber spool. Both of these sys-
modulator, before being re¬‚ected by Faraday mirror. P2 tems are equivalent and exhibit similar performances. In
follows the same path. Alice activates brie¬‚y her modula- addition, the group of Anders Karlsson at the Royal In-
tor to apply a phase shift on P1 only, in order to encode stitute of Technology in Stockholm veri¬ed in 1999 that
a bit value exactly like in the traditional phase coding this technique also works at a wavelength of 1550 nm
scheme. The attenuator is set so that when the pulses (Bourennane et al., 1999 and Bourennane et al., 2000).
leave Alice, they do not contain more than a fraction of a These experiments demonstrate the potential of “plug &
photon. When they reach the PBS after their return trip play”-like systems for real world quantum key distribu-
through the link, the polarization state of the pulses is tion. They certainly constitute a good candidate for the
exactly orthogonal to what it was when they left, thanks realization of prototypes.
to the e¬ect of the Faraday mirror. P1 is then re¬‚ected Their main disadvantage with respect to the other sys-
instead of being transmitted. It takes the long arm to tems discussed in this section is that they are more sensi-
the coupler. When it passes, Bob activates his modula- tive to Trojan horse strategies (see section VI K). Indeed,
tor to apply a phase shift used to implement his basis Eve could send a probe beam and recover it through the
choice. Similarly, P2 is transmitted and takes the short strong re¬‚ection by the mirror at the end of Alice™s sys-
arm. Both pulses reach the coupler at the same time and tem. To prevent such an attack, Alice adds an attenu-
they interfere. Single-photon detectors are then use to ator to reduce the amount of light propagating through
record the output port chosen by the photon. her system. In addition, she must monitor the incoming
We implemented with this set-up the full four states intensity using a classical linear detector. Besides, sys-
BB84 protocol. The system was tested once again on tems based on this approach cannot be operated with a
the same installed optical ¬ber cable linking Geneva and true single-photon source, and will thus not bene¬t from
the progress in this ¬eld 39 .
Nyon (23 km, see Fig. 13) at 1300 nm and observed
a very low QBERopt ≈ 1.4% (Ribordy et al. 1998 and
2000). Proprietary electronics and software were devel-
oped to allow fully automated and user-friendly operation D. Frequency coding
of the system. Because of the intrinsically bi-directional
nature of this system, great attention must be paid to Phase based systems for QC require phase synchroniza-
Rayleigh backscattering. The light traveling in an optical tion and stabilization. Because of the high frequency of
¬ber undergoes scattering by inhomogeneities. A small optical waves (approximately 200 THz at 1550 nm), this
fraction (≈1%) of this light is recaptured by the ¬ber condition is di¬cult to ful¬ll. One solution is to use self-
in the backward direction. When the repetition rate is aligned systems like the “plug&play” set-ups discussed
high enough, pulses traveling to Alice and back from her in the previous section. Prof. Goedgebuer and his team
must intersect at some point along the line. Their inten- from the University of Besan¸on, in France, introduced
c
sity is however strongly di¬erent. The pulses are more an alternative solution (Sun et al. 1995, Mazurenko et al.
than a thousand times brighter before than after re¬‚ec- 1997, M´rolla et al. 1999; see also Molotkov 1998). Note
e
tion from Alice. Backscattered photons can accompany that the title of this section is not completely correct in
a quantum pulse propagating back to Bob and induce the sense that the value of the qubits is not coded in the
false counts. We avoided this problem by making sure frequency of the light, but in the relative phase between
that pulses traveling from and to Bob are not present in sidebands of a central optical frequency.
the line simultaneously. They are emitted in the form
of trains by Bob. Alice stores these trains in her optical
delay line, which consists of an optical ¬ber spool. Bob
waits until all the pulses of a train have reached him, be- 39
The fact that the pulses travel along a round trip implies
fore sending the next one. Although it completely solves that losses are doubled, yielding a reduced counting rate.
the problem of Rayleigh backscattering induced errors,
this con¬guration has the disadvantage of reducing the

28
Their system is depicted in Fig. 19. A source emits to reveal eavesdropping. In addition, it was shown that
short pulses of classical monochromatic light with angu- this reference beam monitoring can be extended to the
lar frequency ωS . A ¬rst phase modulator P MA modu- four-states protocol (Huttner et al., 1995).
lates the phase of this beam with a frequency „¦ ≪ ωS The advantage of this set-up is that the interference
and a small modulation depth. Two sidebands are thus is controlled by the phase of the radio-frequency oscilla-
generated at frequencies ωS ± „¦. The phase modulator is tors. Their frequency is 6 orders of magnitude smaller
driven by a radio-frequency oscillator RF OA whose phase than the optical frequency, and thus considerably easier
¦A can be varied. Finally, the beam is attenuated so that to stabilize and synchronize. It is indeed a relatively sim-
the sidebands contain much less than one photon per ple task that can be achieved by electronic means. The
pulse, while the central peak remains classical. After the Besan¸on group performed key distribution with such a
c
transmission link, the beam experiences a second phase system. The source they used was a DBR laser diode
modulation applied by P MB . This phase modulator is at a wavelength of 1540 nm and a bandwidth of 1 MHz.
driven by a second radio-frequency oscillator RF OB with It was externally modulated to obtain 50 ns pulses, thus
the same frequency „¦ and a phase ¦B . These oscillators increasing the bandwidth to about 20 MHz. They used
must be synchronized. After passing through this device, two identical LiNbO3 phase modulators operating at a
the beam contains the original central frequency ωS , the frequency „¦/2π = 300M Hz. Their spectral ¬lter was
sidebands created by Alice, and the sidebands created by a Fabry-Perot cavity with a ¬nesse of 55. Its resolution
Bob. The sidebands at frequencies ωS ± „¦ are mutually was 36 MHz. They performed key distribution over a
coherent and thus yield interference. Bob can then record 20 km long single-mode optical ¬ber spool, recording a
the interference pattern in these sidebands, after removal QBERopt contribution of approximately 4%. They es-
of the central frequency and the higher order sidebands timated that 2% can be attributed to the transmission
with a spectral ¬lter. of the central frequency by the Fabry-Perot cavity. Note
To implement the B92 protocol (see paragraph II D 1), also that the detector noise is relatively large due to the
Alice randomly chooses the value of the phase ¦A , for large pulse durations. Both these errors could be lowered
each pulse. She associates a bit value of “0” to the phase by increasing the separation between the central peak
0 and the bit “1” to phase π. Bob also chooses randomly and the sidebands, allowing reduced pulse widths, hence
whether to apply a phase ¦B of 0 or π. One can see that shorter detection times and lower darkcounts. Neverthe-
if |¦A ’ ¦B | = 0, the interference is constructive and less, a compromise must be found since, in addition to
Bob™s single-photon detector has a non-zero probability technical drawbacks of high speed modulation, the po-
of recording a count. This probability depends on the larization transformation in an optical ¬ber depends on
number of photons present initially in the sideband, as the wavelength. The remaining 2% of the QBERopt is
well as the losses induced by the channel. On the other due to polarization e¬ects in the set-up.
hand, if |¦A ’ ¦B | = π, interference is destructive and This system is another possible candidate. It™s main
no count will ever be recorded. Consequently, Bob can advantage is the fact that it could be used with a true
infer, everytime he records a count, that he applied the single-photon source, if it existed. On the other hand,
same phase as Alice. When a given pulse does not yield the contribution of imperfect interference visibility to the
a detection, the reason can be that the phases applied error rate is signi¬cantly higher than that measured with
were di¬erent and destructive interference took place. It “plug&play” systems. In addition, if this system is to be
can also mean that the phases were actually equal, but truly independent of polarization, it is essential to ensure
the pulse was empty or the photon got lost. Bob cannot that the phase modulators have very low polarization
decide between these two possibilities. From a concep- dependency. In addition, the stability of the frequency
tual point of view, Alice sends one of two non-orthogonal ¬lter may constitute a practical di¬culty.
states. There is then no way for Bob to distinguish be-
tween them deterministically. However he can perform a
generalized measurement, also known as a positive opera- E. Free space line-of-sight applications
tor value measurement, which will sometimes fail to give
an answer, and at all other times gives the correct one. Since optical ¬ber channels may not always be avail-
Eve could perform the same measurement as Bob. able, several groups are trying to develop free space line-
When she obtains an inconclusive result, she could just of-sight QC systems, capable for example to distribute a
block both the sideband and the central frequency so key between buildings rooftops in an urban setting.
that she does not have to guess a value and does not risk It may of course sound di¬cult to detect single pho-
introducing an error. To prevent her from doing that, tons amidst background light, but the ¬rst experiments
Bob veri¬es the presence of this central frequency. Now demonstrated the possibility of free space QC. Besides,
if Eve tries to conceal her presence by blocking only the sending photons through the atmosphere also has advan-
sideband, the reference central frequency will still have tages, since this medium is essentially not birefringent
a certain probability of introducing an error. It is thus (see paragraph III B 4). It is then possible to use plain
possible to catch Eve in both cases. The monitoring of polarization coding. In addition, one can ensure a very
the reference beam is essential in all two-states protocol

29
high channel transmission over large distances by choos- Before quantum repeaters become available and allow
ing carefully the wavelength of the photons (see again to overcome the distance limitation of ¬ber based QC,
paragraph III B 4). The atmosphere has for example a free space systems seem to o¬er the only possibility for
high transmission “window” in the vicinity of 770 nm QC over distances of more than a few dozens kilome-
(transmission as high as 80% between a ground station ters. A QC link could be established between ground
and a satellite), which happens to be compatible with based stations and a low orbit (300 to 1200 km) satel-
commercial silicon APD photon counting modules (de- lite. The idea is ¬rst to exchange a key kA between Alice
tection e¬ciency as high as 65% and low noise). and a satellite, using QC, next to establish another key
The systems developed for free space applications are kB between Bob and the same satellite. Then the satel-
actually very similar to the one shown in Fig. 12. The lite publicly announces the value K = kA • kB obtained
main di¬erence is that the emitter and receiver are con- after an XOR of the two keys (• represents here the
nected to telescopes pointing at each other, instead of XOR operator or equivalently the binary addition mod-
an optical ¬ber. The contribution of background light ulo 2 without carry). Bob subtracts then his key from
this value to recover Alice™s key (kA = K – kB ) 41 . The
to errors can be maintained at a reasonable level by us-
ing a combination of timing discrimination (coincidence fact that the key is known to the satellite operator may
windows of typically a few ns), spectral ¬ltering (¤ 1 nm be at ¬rst sight seen as a disadvantage. But this point
interference ¬lters) and spatial ¬ltering (coupling into an might on the contrary be a very positive one for the de-
optical ¬ber). This can be illustrated with the follow- velopment of QC, since governments always like to keep
ing simple calculation. Let us suppose that the isotropic control of communications! Although this has not yet
spectral background radiance is 10’2 W/m2 nm sr at been demonstrated, Hughes as well as Rarity have es-
800 nm. This corresponds to the spectral radiance of a timated - in view of their free space experiments - that
clear zenith sky with a sun elevation of 77—¦ (Zissis and the di¬culty can be mastered. The main di¬culty would
Larocca, 1978). The divergence θ of a Gaussian beam come from beam pointing - don™t forget that the satel-
with radius w0 is given by θ = »/w0 π. The product of lites will move with respect to the ground - and wander-
beam (telescope) cross-section and solid angle, which is a ing induced by turbulences. In order to reduce this latter
constant, is therefore πw0 πθ2 = »2 . By multiplying the
2
problem the photons would in practice probably be sent
radiance by »2 , one obtains the spectral power density. down from the satellite. Atmospheric turbulences are in-
With an interference ¬lter of 1 nm width, the power on deed almost entirely concentrated on the ¬rst kilometer
the detector is 6 · 10’15 W, corresponding to 2 · 104 pho- above the earth surface. Another possibility to compen-
tons per second or 2 · 10’5 photons per ns time window. sate for beam wander is to use adaptative optics. Free
This quantity is approximately two orders of magnitude space QC experiments over distances of the order of 2
larger than the dark count probability of Si APD™s, but km constitute major steps towards key exchange with a
still compatible with the requirements of QC. Besides the satellite. According to Buttler et al. (2000), the optical
performance of free space QC systems depends dramati- depth is indeed similar to the e¬ective atmospheric thick-
cally on atmospheric conditions and air quality. This is ness that would be encountered in a surface-to-satellite
problematic for urban applications where pollution and application.
aerosols degrade the transparency of air.
The ¬rst free space QC experiment over a distance of
more than a few centimeters 40 was performed by Jacobs F. Multi-users implementations
and Franson in 1996. They exchanged a key over a dis-
tance of 150 m in a hallway illuminated with standard Paul Townsend and colleagues investigated the ap-
¬‚uorescent lighting and 75 m outdoor in bright daylight plication of QC over multi-user optical ¬ber networks
without excessive QBER. Hughes and his team were the (Phoenix et al 1995, Townsend et al. 1994, Townsend
¬rst to exchange a key over more than one kilometer un- 1997b). They used a passive optical ¬ber network ar-
der outdoor nighttime conditions (Buttler et al. 1998, chitecture where one Alice “ the network manager “ is
and Hughes et al. 2000a). More recently, they even im- connected to multiple network users (i.e. many Bobs, see
proved their system to reach a distance of 1.6 km under Fig. 20). The goal is for Alice to establish a veri¬ably
daylight conditions (Buttler et al. 2000). Finally Rarity secure and unique key with each Bob. In the classical
and his coworkers performed a similar experiment where limit, the information transmitted by Alice is gathered by
they exchanged a key over a distance of 1.9 km under all Bobs. However, because of their quantum behavior,
nighttime conditions (Gorman et al. 2000).


41
This scheme could also be used with optical ¬ber imple-
40
Remember that Bennett and his coworkers performed the mentation provided that secure nodes exist. In the case of a
¬rst demonstration of QC over 30 cm in air (Bennett et al. satellite, one tacitly assumes that it constitutes such a secure
1992a). node.



30
the photons are e¬ectively routed at the beamsplitter to V. EXPERIMENTAL QUANTUM
one, and only one, of the users. Using the double Mach- CRYPTOGRAPHY WITH PHOTON PAIRS
Zehnder con¬guration discussed above, they tested such
an arrangement with three Bobs. Nevertheless, because The possibility to use entangled photon pairs for quan-
of the fact that QC requires a direct and low attenuation tum cryptography was ¬rst proposed by Ekert in 1991.
optical channel between Alice and Bob, the possibility to In a subsequent paper, he investigated, with other re-
implement it over large and complex networks appears searchers, the feasibility of a practical system (Ekert et
limited. al., 1992). Although all tests of Bell inequalities (for a
review, see for example, Zeilinger 1999) can be seen as
experiments of quantum cryptography, systems speci¬-
cally designed to meet the special requirements of QC,
like quick change of bases, were ¬rst implemented only
recently 42 . In 1999, three groups demonstrated quan-
tum cryptography based on the properties of entangled
photons. They were reported in the same issue of Phys.
Rev. Lett. (Jennewein et al. 2000b, Naik et al. 2000,
Tittel et al. 2000), illustrating the fast progress in the
still new ¬eld of quantum communication.
When using photon pairs for QC, one advantage lies
in the fact that one can remove empty pulses, since the
detection of one photon of a pair reveals the presence of
a companion. In principle, it is thus possible to have
a probability of emitting a non-empty pulse equal to
one43 . It is bene¬cial only because presently available
single-photon detector feature high dark count probabil-
ity. The di¬culty to always collect both photons of a pair
somewhat reduces this advantage. One frequently hears
that photon-pairs have also the advantage of avoiding
multi-photon pulses, but this is not correct. For a given

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