Transmitter Design Proposal for the BB84 Quantum Key Distribution

Protocol using Polarization Modulated Vertical Cavity Surface-emitting

Lasers

Ágoston Schranz and Eszter Udvary

Department of Broadband Infocommunications and Electromagnetic Theory, Budapest University of Technology and

Economics, Egry József utca 18., Budapest, Hungary

Keywords:

Quantum Key Distribution (QKD), Vertical Cavity Surface Emitting Lasers (VCSEL), Polarization Switching.

Abstract:

Vertical cavity surface-emitting lasers (VCSELs) have multiple beneﬁcial properties for applications in quantum

key distribution (QKD). However, polarization switching (PS) characteristic of these lasers can be problematic if

it is unwanted. The origin and properties of PS is discussed. We propose a new transmitter design for the BB84

protocol using only two VCSELs – both corresponding to one of the two bases in which polarized photons are

sent –, which are modulated in polarization, purposely generating switches between two orthogonally polarized

modes. Advantages and design difﬁculties of this design are outlined. We also consider the possibility of a

spectral attack, originating from the frequency splitting between these modes, and offer a solution that can

protect the key from eavesdroppers utilizing this kind of attack.

1 INTRODUCTION

Not every message is meant for everyone to access:

cryptography can be used to conceal messages from

unauthorized parties. Once general purpose quantum

computers will be available, the only provably secure

solution is to use one-time pad encryption schemes.

These are uncrackable unless a third person obtains

another copy of the key (Shannon, 1949). Keys, how-

ever, should not be used more than once, therefore it

is needed to agree on a new key before every trans-

mission. Sharing them on a classical channel provides

eavesdroppers an opportunity to access secret informa-

tion, thus the key distribution is a critical task.

Quantum key distribution is the most advanced

ﬁeld of quantum communications. It utilizes the dis-

tinctive features of quantum mechanics, mainly the

Heisenberg uncertainty principle and the no-cloning

theorem (Wootters and Zurek, 1982), to provide prov-

ably secure methods for key distribution. The sender

and the receiver, generally referred to as Alice and Bob,

encode the messages in quantum states. The protocols

are designed so that the presence of an eavesdropper,

called Eve, can be revealed by the communication

parties.

Discrete-variable quantum key distribution (DV-

QKD) protocols, such as BB84 (Bennett and Brassard,

1984), B92 (Bennett, 1992) or E91 (Ekert, 1991) of-

ten use the linear polarization of a single photon as a

qubit. In practice, the implementation of true single

photon sources is still a challenge. Instead, weak co-

herent states (highly attenuated laser pulses) are used

as substitute for single-photon states (Bennett et al.,

1992). In a weak coherent state QKD scheme, semi-

conductor lasers can be used as photon sources. More

conventional edge-emitting lasers (EELs) and vertical-

cavity surface-emitting lasers are both suitable for the

application.

Coherent states follow Poissonian photon statistics

characterized by its mean photon number (Glauber,

1963), analogous to the classical intensity of light. A

Poisson distribution with any parameter

has nonzero

values for any given integer

. However, sending out

more than one photon per pulse can help the eavesdrop-

per perform a photon number splitting attack (Brassard

et al., 2000). In order to minimize the probability of

ﬁnding more than one photon in a single light pulse,

mean photon numbers are calibrated to be much lower

than one. This greatly decreases performance com-

pared to a single photon source, as for mean photon

values lower than

λ = 0.1

there is a probability higher

than 90% to detect zero photons per pulse, effectively

reducing the key rate below one tenth of the pulse

repetition rate.

The problems described above are inherent to all

lasers. Apart from these, EELs and VCSELs exhibit

252

Schranz, Á. and Udvary, E.

Transmitter Design Proposal for the BB84 Quantum Key Distribution Protocol using Polarization Modulated Vertical Cavity Surface-emitting Lasers.

DOI: 10.5220/0006638002520258

In Proceedings of the 6th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2018), pages 252-258

ISBN: 978-989-758-286-8

different favourable and unfavourable properties with

respect to quantum key distribution applications. Sec-

tion 2 focuses on the relative advantages and draw-

backs provided by VCSELs. In Section 3 we propose

a new, simpliﬁed transmitter design for the BB84 pro-

tocol, based on the otherwise problematic polarization

switching mechanism exhibited by some VCSELs,

while in Section 4 the protection against a spectral

attack is outlined.

2 ADVANTAGES AND

DRAWBACKS OF VCSELS IN

QKD SYSTEMS

Surface-emitting lasers, as their name suggests, emit

light perpendicularly to the active region. Therefore,

these devices can be tested on the wafer level, yielding

substantial cost reduction compared to EELs, while

mounting and packaging technologies used for LEDs

can also be utilized. This makes VCSELs a favourable

candidate for most applications. Furthermore, the de-

sign and production of large one or two-dimensional

laser arrays becomes an easy task. (Michalzik, 2013).

There are, however, several other aspects, for which

VCSELs are inherently suitable for quantum key dis-

tribution applications.

2.1 Advantages

VCSELs often have low threshold currents and low

output power compared to conventional edge-emitting

lasers (Michalzik, 2013). DV-QKD applications al-

ways operate in the low-power regime, meaning that

weak laser pulse QKD implementations need exter-

nal attenuation. Lower output power results in less

external attenuation and less wasted power, therefore

VCSELs are more energy-efﬁcient in this regard than

their edge-emitting counterparts.

Moreover, VCSELs’ output beams are typically

characterized by a low divergence angle and symmet-

rical (circular) cross section. These properties support

more efﬁcient coupling to optical ﬁbers as well as

longer distance free space links, compared to higher

divergence elliptical cross-section beams typical of

EELs (Michalzik, 2013). Finally, due to their short

cavity length, surface-emitting lasers usually emit in a

single longitudinal mode. Due to all these favourable

properties, VCSELs are being used in QKD devices

(Vest et al., 2015).

2.2 Disadvantage: Polarization

Switching

The most well-known implementation of a qubit in

single photon based QKD protocols is the polarization

qubit, where information is carried by the polarization

state of a single photon. This makes the protocols

extremely sensitive to polarization errors.

As an example, the earliest QKD protocol, BB84

uses two different two-dimensional orthogonal bases:

the so called rectilinear and the diagonal (Bennett and

Brassard, 1984). In the case of single photon polariza-

tion qubits, the basis vectors of the two bases corre-

spond to linear photon polarizations at angles 0

/90

and ±45°, respectively.

Some VCSELs exhibit a speciﬁc feature uncharac-

teristic of (properly constructed) edge-emitting lasers,

called polarization switching. The highly symmet-

rical design of surface emitting lasers results in no

preferred linear polarization direction. Small and in-

evitable anisotropies, however, almost always choose

two preferred orthogonal directions, corresponding to

the crystallographic axes, along which the light can

be polarized. These two modes have a frequency split

due to birefringence. Above threshold, one of these

modes starts to lase, however, increasing the injection

current may cause an abrupt switch to the orthogo-

nal mode, while staying in the fundamental transverse

mode regime. Switching can occur from the high to

the low frequency mode (Type I) or vice versa (Type

II). The mechanism is also strongly dependent on both

the strength and polarization angle of optical feedback

(Nazhan and Ghassemlooy, 2017).

Original reports by Choquette et al. attributed the

polarization switching to thermal effects: current heat-

ing redshifts the gain curve relative to the mean of the

two different wavelength modes, reversing the gain dif-

ference, thus allowing the originally suppressed mode

to lase (Choquette et al., 1995). Later, San Miguel,

Feng and Moloney developed a rate-equation model,

commonly known as the SFM- or four-level model

(San Miguel et al., 1995), which incorporates magnetic

sublevels and mechanisms that are much faster than

the thermal response (phase anisotropy

caused by

birefringence, amplitude anisotropy

– a product of

both gain anisotropies and dichroism –, the mixing of

carriers with opposite signs of angular momentum or

spin-ﬂip relaxation rate

, saturable dispersion

, etc.).

Martín-Regalado et al. performed an in-depth numer-

ical mode stability analysis based on the model, and

deducted that polarization switches can be explained

with nonzero values of

. Small nonvanishing

values of

are also needed to be in agreement with

experimental ﬁndings (Martín-Regalado et al., 1997b).

Transmitter Design Proposal for the BB84 Quantum Key Distribution Protocol using Polarization Modulated Vertical Cavity

Surface-emitting Lasers

253

Table 1: Example of an error in BB84 caused by unwanted

polarization switching. States

↑

and

carry a logical 1,

→

and

carry a logical 0. Polarization switches occur in bits

#2 and #4, but only the latter appears as an error in the raw

key due to the measurement basis choices.

Bit number 1 2 3 4 5 6

Intended state ↑ & & → ↑ %

Sent state ↑ % & ↑ ↑ %

Meas. basis + + × + × ×

Alice’s raw key 1 0 0 1

Bob’s raw key 1 0 1 1

The critical values of parameters deﬁne different

regions of stability in the parameter space. Most of

these parameters (such as

and

) are built-in and

can only be altered on a fabrication level, or indirectly

changed with the external parameters (injection current

and temperature). Regions where only one polarization

mode (

ˆx

ˆy

), neither of the modes, or both of them

are stable, are reported. Bistable regions are often

accompanied by a hysteresis in switching, also found

experimentally, as the current is ﬁrst increased then

decreased (Kaplan, 2007).

The reason why unwanted polarization switching

is a problem in QKD, can be easily understood in

the framework of the BB84 protocol. Switching can

lead to situations where a photon is sent and measured

in the same basis, but ultimately carries the opposite

bit value as intended. This will cause Alice and Bob

to believe that they share the same raw key bit and

either use it incorrectly as part of the ﬁnal key, or

compare them as part of the sifting process, potentially

arriving at the false conclusion that the bit error rate

has increased and there is an eavesdropper present.

Both of these outcomes are problematic and reduce

the system’s reliability. An example is shown in Table

Apart from QKD, multiple applications, e.g. sens-

ing, optical mice, or communication links where

polarization-dependent elements are used, are sensi-

tive to polarization switching. This need called for

a solution to mass-produce VCSELs with EEL-like

stable linearly polarized emission, without sacriﬁc-

ing any of the beneﬁcial properties mentioned in Sec-

tion 2.1. There have been several different propos-

als and methods to obtain this behaviour. These in-

clude solutions based on polarization-dependent gain,

polarization-dependent mirrors, external optical feed-

back, and asymmetric resonators. The most reliable,

commercially widespread method utilizes surface grat-

ings (Michalzik and Ostermann, 2013).

Controlled on-demand polarization switching has

also found its applications, mostly in all-optical sig-

Figure 1: Trivial BB84 transmitter design using four linearly

polarized lasers.

nal processing, for example shift registers (Katayama

et al., 2016). In the next section, we are proposing a

BB84 transmitter scheme that deliberately takes advan-

tage of the polarization switches, rather than suffering

their consequences.

3 PROPOSAL FOR A NEW BB84

TRANSMITTER DESIGN

3.1 Proposed Design

We propose a new transmitter design for the BB84

protocol that utilizes the polarization switching to of-

fer a simpliﬁed and possibly cost-reducing alternative

to the trivial design shown in Figure 1. The trivial

transmitter contains four individual lasers (EELs or

polarization-stabilized VCSELs) with linear polariza-

tions, oriented along one of the four directions used in

the protocol. This is a very straightforward approach,

where a random stream of selection bits chooses the ba-

sis in which the transmission happens, and the key bits

choose between the two sources lasing in that basis.

Linearly polarized lasers are the most trivial choice

for photon sources in a BB84 transmitter. This way,

one would need four individual devices, all aligned

to one of the four possible output polarization angles

(Figure 1) (Ruiz-Alba et al., 2011). Thus, randomly

selecting a basis chooses between two groups of lasers,

and the key bit to be transmitted determines the needed

polarization and the speciﬁc laser within the group.

In addition to its relative simplicity, advantages to

this transmitter design include that every laser can be

driven by identical current pulses.

As opposed to this, the new design, as depicted

in Figure 2, uses only two VCSELs exhibiting polar-

ization switching. VCSEL 1 is oriented so that its

polarization eigenstates are aligned to the rectilinear

basis vectors, while the eigenstates of VCSEL 2 are

PHOTOPTICS 2018 - 6th International Conference on Photonics, Optics and Laser Technology

254

Figure 2: Proposed new BB84 transmitter design using two

polarization-switchable VCSELs.

aligned to the diagonal basis. Choosing a transmission

basis with the help of selection bits simultaneously

selects one of the two lasers. Key bits are selecting the

desired polarization within the given basis, essentially

modulating the laser in polarization.

The main beneﬁt of our proposed scheme could be

that it only needs two laser diodes (namely VCSELs)

as opposed to four in the trivial design, effectively

reducing the cost and the required space only by in-

troducing a small driving and processing complexity

(different amplitude current impulses, thus different

amount of attenuation for different key bit values). Ad-

ditionally, one would only need to combine two signals

instead of four before transmission.

3.2 Implementation of On-Demand

Polarization Switching

Induced polarization switching in VCSELs has been

extensively studied, and it was found that injection of

external polarized light can be used to switch between

the

ˆx

and

ˆy

-polarized modes on demand (Bandyopad-

hyay et al., 2003). This, however, usually requires a

master laser with ﬁxed linear polarization. Switching

by optical injection would not reduce the number of

necessary lasers in the transmitter, therefore we are

not concerned with this option.

As mentioned in Section 2, most of the parameters

that play a role in the stability of the modes are built-in

properties of the device. Their values can be modeled

either as ﬁxed or as slightly current-dependent (

and

, speciﬁcally) (Martín-Regalado et al., 1997b). The

only parameter, which can be controlled externally, is

the pump parameter

, that is, the injection current

normalized to threshold. We note that although the

original reports named current-induced self-heating

as a cause of PS, the thermal time constants are too

large to achieve a reasonable key rate, therefore we

intend to work at a constant active region temperature,

where switches are expected to occur as well (Martín-

Regalado et al., 1997a).

Current-modulated polarization switching has been

studied throughout the last 25 years. Most of the re-

search focused on VCSELs biased near the switching

current and modulated sinusoidally. Gain-guided circu-

Time [a.u.]

µ [a.u.]

(τ )

ˆx stable

ˆy stable

Figure 3: Different amplitude current pulses for producing

differently polarized light pulses. The bottom line signi-

ﬁes the threshold current

µ = 1

. The

ˆx

-polarized mode is

stable for currents below the dashed line, the

ˆy

-polarized

mode is stable above the dash-dotted line, therefore the low-

amplitude pulse will be mainly

ˆx

-polarized, while the high-

amplitude pulse should be mainly

ˆy

-polarized. A bistable

region, responsible for hysteresis, lies between the two lines.

is the pulse width, while

(τ)

is the smallest current peak

value needed for polarization switching to occur given a

pulse of length τ.

lar VCSELs have been found to possess limited modu-

lation frequencies of about 80 (Choquette et al., 1994)

to 90 kHz (Verschaffelt et al., 2002), mainly attributed

to thermal processes. Contrary to this, switches in

index-guided VCSELs have been observed to be only

partially of thermal origin. These devices can be modu-

lated in polarization at much larger frequencies, mean-

ing that faster mechanisms also play a role in switching

(Verschaffelt et al., 2003). Modulation frequencies up

to 50 MHz have been reported as early as in 1998

(Panajotov et al., 1998).

Speciﬁcally designed VCSELs have also been in-

vestigated. In 1994, Choquette et al. reported that cru-

ciform VCSELs can be modulated with a frequency up

to 50 MHz in polarization using small signal currents

varying around a bias near the switching point. They

also observed that large-signal modulation between

currents just below threshold and above the switching

point causes the originally stable polarization to ex-

hibit a frequency-doubling pulsing at low frequencies.

Increasing the frequency decreases the intensity of the

second output pulse per cycle, which ultimately disap-

pears (Choquette et al., 1994). Asymmetrical current

injection techniques are also promising. A recent study

by Barve et al. showed that the two orthogonally polar-

ized modes of a single VCSEL can be simultaneously

and independently modulated using two asymmetrical

sets of electrodes with a data rate up to 4 Gbps (Barve

Transmitter Design Proposal for the BB84 Quantum Key Distribution Protocol using Polarization Modulated Vertical Cavity

Surface-emitting Lasers

255

et al., 2014). This would make an ideal candidate for

our proposed scheme, as long as the cost increase due

to the special design is sufﬁciently low.

To the best of our knowledge, no extensive studies

concerning the pulsed polarization modulation have

been conducted, neither theoretically, nor experimen-

tally. One mention (Panajotov et al., 1998) states that

the VCSEL under test, exhibiting polarization switch-

ing in CW mode, emitted stable linear polarization

when using short (22 ns) current pulses at a repetition

rate of 1 kHz. The explanation emphasizes the ther-

mal nature of switching, as no current heating can

take place in such a short time interval. In contrast to

this, another study brieﬂy mentions that they observed

switches when they biased the laser at threshold or

well above the DC switching current and used 10 ns

long current pulses (Verschaffelt et al., 2003).

We would like to engage in more in-depth research

concerning pulsed mode polarization modulation in

VCSELs. Figure 3 shows a possible way to select

polarization in a single VCSEL. When the laser starts

emitting just above threshold, the

ˆx

mode is selected.

The pulse on the left is thus

ˆx

-polarized. If a

ˆy

polarized pulse is needed (on the right), the peak value

of the current should be chosen as to at least exceed the

upper border of the bistable region.

(τ)

denotes the

smallest peak current value where switching occurs

given a pulse of length τ.

3.3 Design Difﬁculties

Compared to the trivial transmitter, where each laser

is driven by identical current pulses, this design comes

with additional driving complexity. To obtain output

light pulses with different dominant polarization, dif-

ferent amplitude current impulses are needed to distin-

guish between logical zeros and ones in a certain basis.

This will cause the output power to be different, there-

fore a variable attenuator should be used to attenuate

every output pulse to the same transmitted power. The

speed with which the attenuation value can be altered

may as well be the bottleneck that ultimately limits the

key rate.

Using the polarization selection scheme depicted

in Figure 3, the pulse on the right will only be partially

ˆy

-polarized. The lower this fraction is, the higher the

possibility that the remaining photon after attenuation

ˆx

-polarized, causing the same error that was outlined

in 2. The time evolution of the intensities measured

in the two orthogonal polarizations should also be

examined: if the beginning and/or the end of the output

light pulse is mainly

ˆx

-polarized, gating can be used to

block these portions in order to increase the fraction of

the wanted polarization. In this case, the time proﬁle

Table 2: Solution against the spectral attack: Bit value as-

signment to the low and high frequency modes of identical

VCSELs.

Mode frequency

Bit value

VCSEL 1 VCSEL 2

LOW

0 1

HIGH

1 0

of the low-amplitude pulse needs to be adjusted as

well to maximize temporal overlap between the two,

and prevent potential attacks based on time-of-arrival

measurements.

Another difﬁculty originates from the fact that the

switching parameters differ from VCSEL to VCSEL

even for devices coming from the same manufacturing

process, some of them maybe even lacking this prop-

erty. This means that every individual diode should

be hand-picked and examined, then the corresponding

attenuator needs to be calibrated to achieve the desired

transmission power.

4 SPECTRAL

DISTINGUISHABILITY: A NEW

TYPE OF ATTACK

The frequency split between the two orthogonally po-

larized modes can be in the order of tens of gigahertzes

(Martín-Regalado et al., 1997b), meaning that differ-

ent quantum states emitted by the same VCSEL might

be spectrally distinguishable. (This can be true for the

trivial design as well, but it can easily be countered us-

ing four lasers with largely overlapping spectra.) This

means, that if Eve ﬁnds out the correspondence be-

tween the four states and their respective frequencies,

she can perform a frequency measurement to deter-

mine the basis and the bit value sent by Alice, then

(theoretically) prepare and send a quantum state that

is identical to the original in both frequency and polar-

ization. Thus Eve obtains a perfect third copy of the

key. Without knowledge of the polarization-frequency

correspondence, a destructive frequency measurement

would annihilate the photon and Eve would have to

guess and choose one of the

4! = 24

possible permu-

tations. Choosing wrong would reveal the eavesdrop-

ping, re-sending imperfect quantum states which in

turn increase the error rate calculated by Bob and Alice.

However, the two parties would declare the abortion of

the current key sharing process in the classical channel

and restart it, alerting Eve and allowing her to switch

conﬁgurations. This way, she can ﬁnd out the corre-

spondence in at most 24 turns.

PHOTOPTICS 2018 - 6th International Conference on Photonics, Optics and Laser Technology

256

One solution would be to use VCSELs with a fre-

quency split so low that it cannot be resolved within

experimental accuracy. Another way to counter the

spectral attack is to use two identical VCSELs with

orthogonally polarized modes having the same fre-

quencies

LOW

and

HIGH

. This means that there is

no one-to-one correspondence between frequency and

polarization – in fact, they are independent. There-

fore Eve is unable to gain information by performing

a spectral measurement on the qubits. She can learn

which frequency is assigned to which bit value in a cer-

tain basis after Alice and Bob publicly disclose their

basis choices, but unless she ﬁnds a way to measure

a photon’s frequency without destroying it, the eaves-

dropping would be ineffective without a polarization

measurement, which can be revealed by the protocol.

To offer protection even against non-destructive

frequency measurement attacks, different bit values

can be assigned to the same (low or high) frequency

mode (Table 2) in case of the two lasers, so that the

bit value and the frequency are independent as well.

Note that non-destructive frequency measurements

still change the photon’s wavefunction according to

the time-energy uncertainty relation

∆E · ∆t ≥

. If

the measurement has high precision (small

∆ω =

∆E

∆t

becomes large. This means further problems for the

eavesdropper, because it increases the probability of

detecting the photon in a wrong time bin, thereby the

error rate.

5 CONCLUSION

Vertical cavity surface-emitting lasers have several ad-

vantages over traditional edge-emitting lasers in a low-

power quantum key distribution scheme. However,

their inherent polarization switching mechanism may

cause problems as several protocols use polarization

qubits. This requires the ability to output photons with

controlled polarization. Over the past decades, several

different methods were developed to ﬁx VCSELs’ po-

larization, out of which surface gratings has proven

to provide the best solution without sacriﬁcing the

aforementioned beneﬁcial properties.

Polarization switching, which occurs between two

orthogonal linear polarizations, could also be poten-

tially exploited to simplify QKD transmitters. In this

paper, we proposed a new transmitter design for the

BB84 protocol including only two VCSELs (as op-

posed to four lasers in a trivial design) driven by dif-

ferent amplitude current pulses in order to select the

desired polarization for the output light. Compared to

the trivial BB84 design, this scheme comes with an

extra concern. As the differently polarized modes have

different frequencies, eavesdroppers may perform a

spectral attack. This attack can be negated by using

two identical VCSELs, removing the one-to-one cor-

respondence between frequency and polarization. The

validity of this proposal is still subject to experimental

investigation, the main concern being the maximal key

rate that can be achieved by this transmitter.

ACKNOWLEDGEMENTS

The authors would like to thank Dr. Zsolt Kis for the

helpful suggestions regarding the physics and back-

ground of photon frequency measurements.

This research was supported by the National Re-

search Development and Innovation Ofﬁce of Hungary

within the Quantum Technology National Excellence

Program (Project No. 2017-1.2.1-NKP-2017-00001).

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