High Speed Fiber-Based Quantum Key Distribution using Polarization
Encoding[^1]

Xiao Tang^2^, Lijun Ma, Alan Mink^3^, Anastase Nakassis, Barry Hershman,
Joshua Bienfang,

Ronald F. Boisvert, Charles Clark and Carl Williams

*National Institute of Standards and Technology, 100 Bureau Dr.,
Gaithersburg, MD 20899*

**ABSTRACT**

We have implemented a quantum key distribution (QKD) system with
polarization encoding at 850 nm over 1 km of optical fiber. The
high-speed management of the bit-stream, generation of random numbers
and processing of the sifting algorithm are all handled by a pair of
custom data handling circuit boards. As a complete system using a clock
rate of 1.25 Gbit/s, it produces sifted keys at a rate of 1.1 Mb/s with
an error rate lower than 1.3% while operating at a transmission rate of
312.5 Mbit/s and a mean photon number μ = 0.1. With a number of proposed
improvements this system has a potential for a higher key rate without
an elevated error rate.

**Keywords**: Quantum key distribution, polarization encoding, BB84,
B92, cryptography, one-time pad.

1.  **INTRODUCTION**

A Quantum Key Distribution (QKD) system can create a shared, secret
cryptographic key over unsecured optical links between two users. In
1984 Bennett and Brassard \[1\] proposed their quantum key distribution
protocol, BB84. A simplified version, B92, was published in 1992 \[2\].
Since then, a number of groups have developed experimental QKD systems,
which were described in a comprehensive review article \[3\]. These QKD
systems were either operating in free-space \[4,5\] or over optical
fiber \[6,7\]. The first study of fiber based QKD at 810 nm wavelength
was reported in 1994 \[8\]. The security of the shared secret key
afforded by QKD is guaranteed by the fundamental quantum properties of
single photons. The generation of secret key at high speed and in real
time would enable the use of one-time pad cryptography, which provides
provable security.

Effective detection of single photons is a critical issue in QKD
development. Currently Ge or InGaAs based avalanche photo diodes (APDs)
are used to detect single photons at telecom wavelengths (1550 and 1310
nm). But their detection efficiency is low and their operating speed is
seriously limited by after-pulsing and a long recovery time (dead time)
in the APD after an avalanche process. Silicon based APDs have much
better performance but they can only detect photons at visible or near
IR wavelengths shorter than about 1000 nm. At these shorter wavelengths,
a single mode telecom fiber has high loss and becomes multimodal, thus
limiting the potential transmission distance. However, these Si-APDs may
be used in QKD systems integrated into local area networks (LANs).
Gordon et al \[9\] have reported a detailed study on an experimental
polarization encoding QKD system at 850 nm with Si-APD using standard
telecom fiber. The longest fiber length they reported was about 11 km.

At NIST, a free-space polarization encoding QKD system operating over a
730 m link was developed in 2004 \[4\]. Using the infrastructure from
that free-space system, we implemented a fiber-based polarization
encoding QKD system operating over 1 km of optical fiber with a
synchronized clock rate of 1.25 GHz. This fiber-based system uses 850 nm
VCSELs as the light source and Si-APDs for the single photon detectors.
Like the free-space system, the fiber-based system is designed to
implement the four-state BB84 protocol with linear-polarization states,
but our initial demonstration is based on B92. The sifted key rate of
our QKD system is expected to double once upgraded to the BB84 protocol.
Executing the B92 protocol and operating at a data transmission rate of
312.5 Mbit/s and an average photon number μ = 0.1, a sifted key rate of
1.1 Mbit/s is achieved with an error rate lower than 1.3%. After error
correction and privacy amplification secure keys are generated. In this
paper, we discuss the design and performance analysis of this
fiber-based polarization encoding QKD system.

2.  **SYSTEM CONFIGURATION**

The NIST fiber-based polarization encoding QKD system is similar to the
NIST free space system \[4\]. The experimental configuration is shown in
figure 1. Alice and Bob are PC-based commercial off the shelf computers
using a Linux operating system. A pair of custom high-speed data
handling circuit boards were designed and implemented at NIST. The
boards communicate with Alice and Bob via their PCI bus. On each board,
there is a field-programmable gate array (FPGA) and gigabit Ethernet
serializers/deserializers (SerDes): one for the classical channel and
four for the quantum channel. A 1.25 Gbit/s CWDM transceiver at each end
of 1 km of SMF-28 fiber is used to form the bi-directional classical
channel at 1510 nm and 1590 nm. Alice's board generates classical and
quantum data-streams at a synchronized 1.25 GHz. Bob's board recovers
and synchronizes to that clock from the received classical channel
data-stream, which uses a standard 8B/10B encoding scheme.

Alice and Bob are also connected via a unidirectional quantum channel
that is parallel to the classical channel. In order to take advantages
of the high speed 10 Gbit/s multimode VCSELs and the high speed, high
detection efficiency of Si-APDs, a wavelength of 850 nm is used for the
quantum channel. When executing the B92 protocol, Alice randomly fires
pulsed light polarized at +45 degree in path 0 and vertical in path 1,
see figure 1. In each path the light from the VCSELs is coupled into a
multimode fiber and then attenuated by a variable optical attenuator
(VOA). The attenuation is carefully adjusted to yield a mean photon
number μ = 0.1 at Alice's output. The attenuated light is then coupled
into a single mode 850 nm fiber patchcord and collimated into
free-space. After one beam passes through a vertically (V) oriented
polarizer and the other through a +45 degree oriented polarizer, they
are combined via a non-polarizing beam-splitting cube (NPBS) and then
coupled into a single mode fiber (Corning HI780, 1 km). After
attenuation, this results, on average, in only one photon in every 10
pulses that leaves from Alice. At the receiver, Bob, a 1 x 2
non-polarizing single mode fiber coupler performs a random choice of
measuring polarization states: either horizontal or -45 degree, which
corresponds to bit values of "0" or "1". A fiber polarization controller
(P.C.) is installed in each branch (path 0 and path 1) of the fiber
coupler to recover the photon's polarization state. In each path, single
photons are measured by a polarizing beam-splitting cube (PBS). After
the PBS an interference filter (I.F.) is used to remove noise at other
wavelengths. Finally, the photons are coupled into a 62.5 μm multimode
fiber and then focused on to the surface of the Si-APD for detection.

![](media/image1.wmf)

Figure 1. Experimental setup

The FPGA on Alice's board, see figure 2(a), generates and stores a
bit-stream of pseudo random data at up to 1.25 Gbit/s. Every 2048 bits
are grouped in a packet, where the 0's trigger VCSEL0 to produce a 45
degree polarization and the 1's trigger VCSEL1 to produce a vertical
polarization. The data rates used in our measurements correspond to a
photon pulse repetition rate at 312.5 or 156.25 Mbit/s (1/4 or 1/8 of
the clock rate). Alice sends a synchronizing message to Bob on the
classical channel at the beginning of each quantum packet. Bob's FPGA,
see figure 2(b), searches for the rising edge of detected photon signals
from the APDs. For each detection event, the packet number and bit
position within the packet (and basis value for BB84), but not the bit
value, of the detected photons are returned to Alice over the classical
channel. Alice's FPGA matches each detection event with the
corresponding event of the stored bit-stream. The matched results, again
without the bit values, are sent back to Bob to confirm reception and
then both Bob and Alice send the bit values to their CPUs for
reconciliation and privacy amplification \[10\] to generate their shared
secret keys. The quantum error rate can be measured in real time from
the raw data before reconciliation.

![](media/image2.jpeg){width="3.0076388888888888in"
height="1.9145833333333333in"}
![](media/image3.jpeg){width="3.0868055555555554in"
height="1.867361111111111in"}

\(a\) Alice (b) Bob

Figure 2. Block diagram of the high-speed data handling printed circuit
boards at Alice and Bob

3.  **EXPERIMENTAL RESULTS AND ANALYSIS**

    1.  **Polarization Recovery**

In a polarization encoding QKD system the polarization state of a photon
carries quantum key information. When a photon travels in free space its
polarization state does not change, if air turbulence is negligible.
However, when a photon travels in an optical fiber its polarization
state is subjected to changes. There are three main causes for problems
with polarization encoding in fiber-based systems \[11\]: first,
transporting a vector (polarization) along a curve (fiber); second,
changes in mechanical stress that cause birefringence; and third,
polarization dependent losses in optical components used in the system.
If the fiber link is well secured and stable, the first problem may be
eliminated. Birefringence in fiber is due to three main sources: (1)
birefringence introduced in the manufacturing process (such as shape and
inner strain), (2) elastic birefringence introduced by mechanical force
(such as bending, lateral stress and torsion) and (3) electric and
magnetic birefringence \[12\]. The birefringence change is usually
caused by the change of mechanical stress in the fiber due to
environmental variation such as of temperature or vibration, depending
on the mechanical and thermal stability of the environment. Temperature
changes are usually quite slow, on the order of tens of minutes.
Vibration changes can occur more frequently, possibly on the order of
seconds. Another effect of the birefringence is the polarization mode
dispersion (PMD). PMD limits the minimal usable pulse length of the
laser; however, this problem can be avoided if a laser with a coherence
time longer than the polarization mode delay is used \[11\]. We can
avoid the third problem by choosing suitable optical components or
compensating for the error as long as we know the polarization
characteristics of the optical components used.

Although the polarization state changes when photons pass through a
fiber, the relation between the two non-orthogonal polarizations is not
changed after they traveled in the same path. At the fiber output, when
a polarization controller recovers one of the two non-orthogonal
polarizations the other is also transformed to a state that has the same
relation with respect to the PBS as they were at the fiber input. Manual
polarization controllers are used in our QKD system to recover the
polarization state for each path in the quantum channel independently at
the output of the fiber.

In the system, when linearly polarized light with a high degree of
polarization (DOP, the ratio of polarized light to non-polarized light)
at Alice travels through the fiber to Bob its polarization orientation
is changed and the DOP may also deteriorate as well. A polarization
extinction ratio (in decibel) for the system is defined as the minimum
counts divided by the maximum counts of orthogonal polarized photons
detected by the APD when the polarization controller is properly
adjusted. A poor extinction ratio will yield high crosstalk and
therefore a high error rate. Based on the B92 protocol, the polarization
state of the PBS is set to be non-conjugated to the polarization state
of the photons from its own path (45 degree), and to be conjugated to
the polarization state of the photons from the other path to block the
crosstalk. Considering the detection probability of the non-conjugated
quantum is 0.5, the probability of the conjugated quantum should be less
than 0.005 in order to reduce the extinction ratio-related error rate to
1%. In that case, the extinction ratio of the system should be better
than 23 dB.

The system extinction ratio is determined by the extinction ratio of
polarizing components in the system (polarizers at Alice and PBSs at
Bob) and the depolarization in the photon-traveling path (fiber and
other optical components such as NPBS). However, the 50/50 NPBS cube
distorts the polarization state, especially for the reflected beam.
Though the NPBS cube balances the power of p and s light components, it
does not fully maintain their phases. We measured the extinction ratio
of a light beam linearly polarized at 45 degree and reflected in an NPBS
to be just 17 dB. So, we configured the 45 degree polarized light to
pass straight through the NPBS cube and the vertically polarized light
to be reflected by the cube. Bob's polarization controllers not only
compensate for the polarization changes in the fiber, but also the phase
distortion in the NPBS. The system extinction ratio can reach as high as
30 dB, which approaches the limitation of the value for the polarizing
components themselves. This result shows the fiber and optical
components in the system can be chosen to have a negligible effect on
the degree of polarization.

Our experiments in the lab show that the extinction ratio can be kept
above 23 dB for as long as 2-3 hours after the initial setup. However,
for field application or longer distance, the extinction ratio will
deteriorate faster. In this case an auto-compensation system is
necessary. We continue to investigate auto-compensation schemes.

2.  **Noise reduction**

Some minor noise pulses appear along with each data pulse when the
transmission distance increases in the quantum channel. Figure 3(a)
shows the main data pulse followed by some noise pulses after 1 km
transmission in the QKD system. Please note that the word "pulse" used
in this section is actually a histogram of accumulated photon counts.
The "pulse width" corresponds to system timing jitter. In the
polarization recovery adjustment process, we find that the polarization
states of these noise pulses are different from the main pulse and
different from each other. The amplitude of the largest noise pulse is
about 2 orders of magnitude smaller than the main pulse.

The noise pulses deteriorate the performance of the system because they
have different polarization states and they broaden the pulse width,
therefore the crosstalk and jitter are increased. We found the
wavelength of these noise pulses is different from that of the main
pulse. These noise pulses can be removed completely by inserting an
interference filter (bandwidth of 5 nm centered at 850 nm) when HI780
fiber is used, see figure 3(b). More detailed study is needed to
identify the cause of these noise pulses.

Figure 3. The response pulses via 1 km 850nm single-mode fiber

To make QKD systems more practical, the fiber should be compatible with
fibers commonly used in standard telecommunication networks. We
experimented with 1 km of SMF-28 fiber for the quantum transmission at
850 nm. Since the cutoff wavelength of the fiber is much longer than 850
nm, some higher order transverse modes exists in the fiber, see Figure
4(a). The higher order mode travels slightly slower than the fundamental
mode (2.3 ns delay in our case). Also its polarization state is
different from that of the fundamental mode. The amplitude of the higher
order mode could be higher than the minimal amplitude of the fundamental
mode. The pulse of the higher order mode becomes a lower limit on the
system extinction ratio. This pulse could be counted in an adjacent time
window when the transmission data rate is high enough. These effects
increase the error rate. With the SMF-28 fiber being fusion spliced to a
piece of HI780 fiber, which functions as a spatial filter, the higher
order mode is greatly suppressed, see Figure 4(b). Other groups also
reported similar approaches to filter the noise from higher modes \[9,
13\]. After removing the noise pulse from the higher order mode, the
classical channel and the quantum channel are able to share a single
standard telecom fiber by using 850/1550 nm WDMs.

![](media/image4.png){width="3.4299212598425197in"
height="2.099212598425197in"}![](media/image5.png){width="3.3811023622047243in"
height="2.1271653543307085in"}

3.  **Transmission data rate**

Transmission data rate is an important performance parameter for a QKD
system, since higher transmission data rates can yield more encryption
keys and enhance the communication capacity. Our custom high-speed data
handling boards on both Alice and Bob provide sifted data directly to
the CPU for error correction and privacy amplification, which can then
be used by application-level data encryption. Hence, we use the sifted
key rate from the boards as one of our quantum performance metrics. The
sifted key rate can be estimated by the following equation:

$R = \mu \cdot L_{f} \cdot L_{c} \cdot L_{d} \cdot \text{Pd} \cdot L_{o} \cdot \nu$
(1)

Where R is the sifted key rate, *μ* is the mean photon number per pulse
at the output of Alice. This parameter is set to 0.1 (10 dB) as is
common in the literature. In this case, 9% of the pulses contain a
single photon, less than 1% contains more than one photon, and the rest
of the pulses are negligible according to Poisson statistics. A higher
mean photon number leads to a higher sifted key rate but more pulses
will contain more than a single photon and will require a higher degree
of privacy amplification. A lower *μ* reduces the sifted key rate. When
the sifted key rate is too low the dark counts of the APD will cause
high error rates. *L~f~* is the optical loss of the fiber. We use 1 km
HI780 fiber and its nominal loss at 850 nm is about 2.3 dB/km. The
actual measured value is about 3 dB, including the losses due to three
connectors and other losses, such as bending. *L~c~* and *L~d~* are the
losses in the 50/50 coupler and the transmission loss at PBS. The *Pd*
is the photon detection efficiency of the APDs. According to the
specifications, this value is about 45% (3.5 dB) at 850 nm. Other
losses, *L~o,~* in the system are about 2 dB. *ν* is the quantum data
repetition rate.

Table 1. Photon budget

  --------------------- ---------- --------------------------------------
                        Value (dB) Comments

  Mean photon number    10         0.1 photon per pulse
  (*μ*)                            

  Loss in fiber         3          2.3 dB/km and loss on connectors and
  (*L~f~*)                         bending

  Loss in coupler       3          1x2 50/50 non-polarizing coupler
  (*L~c~*)                         

  Loss on detection     3          Transmission possibility for a photon
  (*L~d~*)                         polarized at 45 degree

  Efficiency of APD     3.5        45% of APD detection efficiency at 850
  (*Pd*)                           nm

  Other loss (*L~o~*)   2          Other loss in the system, such as
                                   filters

  Total                 24.5       
  --------------------- ---------- --------------------------------------

The values of these losses in our system are shown in Table 1, which
yield a total loss of about 24.5 dB. When Alice sends quantum data at a
repetition rate, *ν,* of 312.5 Mb/s and 156.25 Mb/s to Bob, we achieve
1.1 Mb/s and 0.6 Mb/s sifted key rate, respectively, which correlates
well with equation (1).

4.  **Quantum Error Rate**

The quantum channel error rate, also called quantum bit error rate
(QBER), is defined as the ratio of incorrect counts to total counts that
are recorded at Bob's APDs. The quantum errors are mainly caused by the
following factors: (1) The dark count rate of the APD and light leakage
into the system, (2) Cross-talk caused by an imperfect polarization
extinction ratio of the system, (3) Temporal jitter of the system.

The first factor is caused by a thermo-initiated avalanche process in
the APD and some unexpected photon detections. It is independent from
the system clock and the data rate. The dark counts of the APD used in
our system are at the order of 10^2^ per second. With proper light
sealing and filtering, the counts due to light leakage are only a few
tens per second. When compared to our Mbit/s data rates, this first
factor is negligible.

The second factor is caused by the imperfect polarization extinction
ratio of the PBS, the polarization recovery unit and an unstable
condition of the fiber. The extinction ratio of the PBS is about 30 dB.
In the best case, the manual polarization controllers can be adjusted to
get a system extinction ratio of 30 dB, however, the system extinction
ratio was measured to be between 23-28 dB during our experiments. So
this factor contributes about 1% of error to the QKD system. It is also
independent from the system clock and data rate.

![](media/image6.jpeg){width="5.160416666666666in"
height="3.9854166666666666in"}

Figure 5. Jitter in the quantum channel

The jitter in the classical channel is mostly caused by electronic
elements in the circuit boards and the CWDM transceivers. The jitter in
the quantum channel is mainly from VCSELs and their drivers as well as
the APDs. Figure 5 shows the jitter in the quantum channel, measured
with a repetitive data stream, is about 167 ps (standard deviation),
which is small enough to guarantee the pulse can be contained within an
800 ps clock period. However, the observed pulses are spread over two
clock periods (1.6 ns). We believe this is caused by a timing
misalignment between the classical channel and the quantum channel since
we can currently only align the timing with an accuracy of 800 ps. A
finer timing adjustment is needed to ensure the data pulse can be kept
within a detection time window of 800 ps. For this reason our QKD system
was operated with a data repetition rate of 312.5 or 156.25 Mbit/s to
ensure the pulses will not be skewed to the adjacent pulse spaces. This
results in an error rate of about 1.2-1.3%. If the jitter is much
smaller than the photon pulse period, the error rate is mainly caused by
an imperfect polarization extinction ratio. With improvements to the
jitter, the system should be able to run at a higher data repetition
rate without an elevated error rate.

4.  **CONCLUSION**

We have implemented a polarization encoding quantum key distribution
system over 1 km of optical fiber. To our knowledge, as a complete
system, the NIST fiber based polarization encoding QKD testbed currently
runs at the highest sifted key rate, more than 1 Mbit/s over 1 km with μ
= 0.1 and an error rate lower than 1.3%. When the photon pulse and its
tail are kept well within the detection time window the quantum error
rate is mainly caused by an imperfect system extinction ratio. An
automatic polarization control unit is necessary to maintain a high
enough extinction ratio for practical applications. An interference
filter removes noise at other wavelengths while the spatial filtering
procedure removes noises due to higher order modes generated in standard
telecom fiber. That means standard telecom fiber can be used to transmit
single photons at 850 nm for a polarization encoding QKD system. The
overall system jitter limits the maximum data rate, thereby limiting the
sifted key rate. An improved VCSEL triggering unit and APD detection
module with less jitter will increase the sifted key rate. At these
higher speeds, with these proposed improvements, integration of QKD and
standard telecom systems may become practical. These are the research
directions we plan to pursue.

**ACKNOWLEDGEMENT**

This work was supported in part by the Defense Advanced Research
Projects Agency under the DARPA QuIST program.

**REFERENCES**

1.  C. H. Bennet and G. Brassard, "Quantum cryptography: Public key
    distribution and coin tossing" in Proc. of the IEEE Int. Conf. on
    Computers, Systems & Signal Processing, pp. 175-179, Bangalore,
    India, December 10-12, (1984).

2.  C. H. Bennett, "Quantum cryptography using any two nonorthogonal
    states," Phys. Rev. Lett., 68, 3121-3124 (1992).

3.  N.Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum
    cryptography" Rev. Mod. Phys. Vol. 74, 145\~195 (2002).

4.  J.C. Bienfang, A. J. Gross, A. Mink, et al. "Quantum key
    distribution with 1.25 Gbps clock synchronization", Optics Express.
    Vol. 7 (9), 2011 (2004).

5.  J. G. Parity, P. R. Tapster and P. M. Gorman, " Secure Free-space
    key-exchange to 1.9 km and beyond", Journal of Modern Optics, vol.
    48, 1887-1901 (2001).

6.  Gobby C., Z. L. Yuan, and A. J. Shields, "Quantum key distribution
    over 122 km of standard telecom fiber", Applied Physics Letters,
    Vol. 84, 3762-3764 (2004).

7.  D. S. Bethune, M. Navarro and W. P. Risk "Enhanced autocompensating
    quantum cryptography system", Applied Optics, Vol. 41, 1640-1648
    (2002).

8.  J. Breguet, A. Muller and N. Gisin, "Quantum cryptography with
    polarized photons in optical fibers, experiment and practical
    limits", Journal of Modern Optics, vol. 41, 2405-2412 (1994).

9.  Karen J. Gordon, Veronica Fernandez, Paul D. Townsend, and Gerald S.
    Buller, "A Short Wavelength GigaHertz Clocked Fiber-Optic Quantum
    Key Distribution System", IEEE J. of Quantum Electronics, Vol. 40,
    900-908 (2004).

10. A. Nakassis, J. Bienfang, and C. Williams, "Expeditious
    reconciliation for practical quantum key distribution," to appear in
    Quantum Information and Computation II, Proc. SPIE 5436 (2004).

11. Hoi-Kwong Lo, Sandu Popescu and Tim Spiller (editors), *Introduction
    to Quantum Computation and Information*, P122, World Scientific
    (1998).

12. Serge Huard, *Polarization of Light*, John Wiley & Sons, Masson
    (1997).

13. Paul D. Townsend, "Experimental Investigation of the Performance
    Limits for First Telecommunications-window Quantum cryptography
    Systems", IEEE Photonics Technology Letters, Vol. 10, No.7,
    1048-1050 (1998).

[^1]: The identification of any commercial product or trade name does
    not imply endorsement or recommendation by the National Institute of
    Standards and Technology.

    ^2^ xiao.tang@nist.gov; phone 301-975-2503; www.nist.gov

    ^3^ alan.mink@nist.gov; phone 301-975-5681; www.nist.gov