Table Of ContentSpringer Theses
Recognizing Outstanding Ph.D. Research
Nurul T. Islam
High-Rate,
High-Dimensional
Quantum Key
Distribution Systems
Springer Theses
Recognizing Outstanding Ph.D. Research
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Nurul T. Islam
High-Rate,
High-Dimensional Quantum
Key Distribution Systems
Doctoral Thesis accepted by Duke University, Durham,
NC, USA
123
NurulT.Islam
DepartmentofPhysics
DukeUniversity
Durham,NC,USA
ISSN2190-5053 ISSN2190-5061 (electronic)
SpringerTheses
ISBN978-3-319-98928-0 ISBN978-3-319-98929-7 (eBook)
https://doi.org/10.1007/978-3-319-98929-7
LibraryofCongressControlNumber:2018953017
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Thisdissertationisdedicatedtomyparents.
Supervisor’s Foreword
Dr. Nurul T. Islam’s thesis describes a broad research program on the topic of
quantum communication. Here, a cryptographic key is exchanged by two parties
usingquantumstatesoflightandthesecurityofthesystemarisesfromthefunda-
mental properties of quantum mechanics. Dr. Islam develops new communication
protocols using high-dimensional quantum states so that more than one classical
bit is transferred by each photon. This approach helps circumvent some of the
non-ideal properties of the experimental system, allowing him to achieve record
key rates on metropolitan distance scales. Another important aspect of the work
is the encoding of the key on high-dimensional phase-randomized weak coherent
states, combined with the so-called decoy states to thwart a class of possible
attacks on the system. The experiments are backed up by a rigorous security
analysis of the system, which accounts for all known device non-idealities. Dr.
Islam goes on to demonstrate a scalable approach for increasing the dimension of
the quantum states and considers attacks on the system that use optimal quantum
cloning techniques. The thesis captures the current state of the art of the field
of quantum communication in laboratory systems and demonstrates that phase-
randomizedweakcoherentstateshaveapplicationbeyondquantumcommunication.
In greater detail, the introductory Chap.1 introduces the basics of cryptography
andpointstotheneedforpost-quantumcryptographicmethodsthatwillbesecure
in the presence of an attacker with a large-scale quantum computer. Quantum
key distribution offers one potential solution, but additional research is needed
to improve the secure key rate of these systems and to analyze their security
in the presence of experimental imperfections. The chapter then introduces the
dissertation, highlighting the original contributions to the field. Chapter 2 is a
pedagogicalintroductiontoquantumkeydistributionusingtwo-dimensional(qubit)
time-phasestates.Here,aquantumphotonicwavepacketisinoneoftwocontingent
timeslotsinthecommunicationsystem(temporalbasis)orinbothtimeslotswitha
relativephasedifference(phasestates).Thereaderiswalkedthroughaquantumkey
distributionsessionusingthesestatesandsomepossibleattacksbyaneavesdropper
are discussed. The chapter is rounded out by discussing a possible experimental
realizationofaquantumkeydistributionsystem,highlightinghowthephasestates
vii
viii Supervisor’sForeword
can be measured at the receiver using thermally insensitive delay interferometers
(describedingreaterdetailinAppendicesAandB).Athoroughdiscussionofafour-
dimensional time-phase quantum key distribution system is presented in Chap.3.
Here,Dr.Islamusedphase-randomizedweakcoherentstatesatthetransmitterand
identifies the fraction of the transmitted states for which the photonic wavepacket
hasoneorlessphotonsusingthedecoy-stateprotocol.Acurrentrecord-highsecure
rateisobtainedwiththissystemforchannellossesusefulforametropolitan-scale
quantum key distribution network. Dr. Islam achieved this result by paying strict
attention to experimental non-ideal behaviors, especially single-photon detector
saturation. The experimental work is complemented with a full security analysis
using entropic uncertainty relations, a state-of-the-art theoretical approach for this
problem with additional details given in Appendix C. Following in Chap.4 is a
security analysis for a quantum key distribution system does not use all quantum
states. A quantum key distribution system is secured using at least two mutually
unbiased bases. For a d-dimension system, there are d states in each basis and
each state on both bases needs to be chosen randomly and sent by transmitter. An
analysis is presented here to show that only d states in one basis and one state in
the other basis need to be used without substantial loss in key rate provided that
the quantum bit error rate is low. This result is important for practical application
for high-dimensional quantum key distribution systems and can be applied to any
quantum photonic states. Going beyond a four-dimensional Hilbert space used in
Chap.3, Dr. Islam presents in Chap.5 a new method for measuring phase states
using a weak local oscillator and two-photon interference at the receiver. This
approach does not require delay interferometers and hence is readily scaled to
higher dimensions. Using this system along with the efficient security approach
described in Chap.4, Dr. Islam observes that detector saturation reduces the key
rate at low channel loss; increasing the dimension helps avoid saturation effects,
but eventually lowers the rate for large dimension. Thus, the secure key rate is
optimizedforadimensionthatisalwayslargerthantwoforthissystem.Chapter6
describesonetypeofattackonahigh-dimensionalquantumkeydistributionsystem
enabled by optimal quantum cloning. Previous experiments on optimal quantum
cloninguseheraldedsingle-photonstatesgeneratedbyparametricdownconversion.
Here, Dr. Islam demonstrates that optimal quantum cloning is also possible using
phase-randomizedweakcoherentstateswiththedecoy-stateprotocol,whichiswell
matchedtothetransmitterusedinthequantumkeydistributionsystem.Consistent
with previous work, the fidelity of the cloned state decreases with dimension and
hencethesecurityofthesystemincreasesassumingconstantbiterrorrate.Finally,
Dr. Islam summarizes his original contributions and points to future directions in
thefinalconclusionchapter.
Columbus,OH DanielJ.Gauthier
Acknowledgments
Iwouldliketoacknowledgetheguidanceandsupportofmyadviser,Prof.Daniel
Gauthier. Over the last 4 years, I have greatly appreciated and benefited from the
amount of time he dedicates to his students, the way he motivates and encourages
everyonetocollectbetterdata,andtherateatwhichherespondstoemailqueries.
Itisanabsoluteprivilegetolearnunderhisguidance.IwouldliketothankDanfor
puttingupwithmeoverthelast4years,andhiswillingnesstocontinuetodoso.
IwouldalsoliketoacknowledgethesupportofProf.JungsangKim,whoafter
Dan moved to OSU, provided me with a lab space, equipment, and an incredible
environment to work. I would also like to thank him for realizing that the high-
efficiencysingle-photondetectorswerecriticalfortheseprojects.Onthesamenote,
I would also like to thank Clinton Cahall for his work on the cryogenic readout
circuitsthatIhaveusedtocollectmostofthedatapresentedhere.Finally,Iwould
liketothankDr.CharlesCiWenLimforteachingmethebasicsofsecurityproofs
and for patiently explaining to me why I should always check my intuition with
calculation.
I am grateful to my preliminary and thesis committee members, Prof. Harold
Baranger,Prof.KateScholberg,andProf.HenryEveritt,forthehelpfuldiscussion
andquestionsandfortakingthetimetoreadthroughthiswork.
I would like to acknowledge all the past members of the Qelectron research
group who overlapped a portion of their graduate school or postdoctoral life with
me—Michael, Bonnie, Hannah, Andres, Otti, Lou, David, Nick—and the only
other present member Meg, for all the conversations, laughter, physics-related
discussions,etc.
Duringgraduateschool,itisveryeasytoloseperspectiveonthebiggerpicture
oflife.IwouldliketothankAryaRoyforconstantlyremindingmeofthat,andall
the free coffee and great conversations about history, politics, sports, and physics.
Forthesamereasons,averyspecialthankstomyfriendsofgrads13—Gleb,Yingru,
Agheal, Ming—who kept me going with frequent lunch meetings and hangouts. I
wouldliketothankPayalforthecompanyduringlongworkdaysandeveningsand
forproofreadingmostofthisthesis.
ix
x Acknowledgments
I also want to thank my college Professors, Dr. Harmon and Dr. Haring-Kaye,
for constantly checking-in with me during my time at Duke. I want to thank Mrs.
Harmon for all the free food and care. Finally, I would like to thank my parents
andsisterfortheirconstantsupport,understanding,andpatience.Theyhavealways
managedtokeepmeshieldedfromtheday-to-dayactivitiesathome.
I would like to gratefully acknowledge the support of the Office of Naval
Research MURI program on Wavelength-Agile Quantum Key Distribution in a
Marine Environment, Grant # N00014-13-1-0627, for funding my research work
atDuke.
