Now that fundamental quantum principles of indeterminacy and measurement have become the basis of new technologies that provide secrecy between two communicating parties, there is a need to provide teaching laboratories that illustrate how these technologies work. In this article, we describe a laboratory exercise in which students perform quantum key distribution with single photons, and see how the secrecy of the communication is ensured by the principles of quantum superposition and state projection. We used a table-top apparatus, similar to those used in correlated-photon undergraduate laboratories, to implement the Bennett-Brassard-84 protocol with polarization-entangled photons. Our experiment shows how the communication between two parties is disrupted by an eavesdropper. We use a simple quartz plate to mimic how an eavesdropper intercepts, measures, and resends the photons used in the communication, and we analyze the state of the light to show how the eavesdropper changes it.
REFERENCES
1.
F. W.
Stauch
, “
Resource letter QI-1: Quantum information
,” Am. J. Phys.
84
, 495
–507
(2016
).2.
M. A.
Nielsen
and
I. L.
Chuang
, Quantum Computation and Quantum Information
(
Cambridge U. P
.,
Cambridge
, 2000
).3.
E. J.
Galvez
, “
Resource letter SPE-1: Single-photon experiments in the undergraduate laboratory
,” Am. J. Phys.
82
, 1018
–1028
(2014
).4.
P. A. M.
Dirac
, The Principles of Quantum Mechanics
, 4th ed. (
Oxford U. P
.,
Oxford
, 1930
).5.
C. A.
Fuchs
and
A.
Peres
, “
Quantum-state disturbance versus information gain: Uncertainty relations for quantum information
,” Phys. Rev. A
53
, 2038
–2045
(1996
).6.
S.
Loepp
and
W. K.
Wooters
, Protecting Information: From Classical Error Correction to Quantum Cryptography
(
Cambridge U. P
.,
Cambridge
, 2006
).7.
8.
S.
DeVore
and
C.
Singh
, “
Development of an interactive tutorial on quantum key distribution
,” in Proceedings of the Physics Education Research Conference
, Minneapolis, MN, 2014
, pp. 59
–62
.9.
A.
Kohnle
and
A.
Rizzoli
, “
Interactive simulations for quantum key distribution
,” Eur. J. Phys.
38
, 035403
(2017
).10.
A. N.
Utama
,
L.
Jianwei
, and
M. A.
Seidler
, “
A hands-on quantum cryptography workshop for pre-university students
,” Am. J. Phys.
(in press, 2020
).11.
12.
13.
W. K.
Wootters
and
W. H.
Zurek
, “
A single quantum cannot be cloned
,” Nature
299
, 802
–803
(1982
).14.
J. S.
Townsend
, A Modern Approach to Quantum Mechanics
(
University Science Books
,
CA
, 2012
).15.
16.
C. H.
Bennett
,
G.
Brassard
,
C.
Crépeau
,
R.
Jozsa
,
A.
Peres
, and
W. K.
Wootters
, “
Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
,” Phys. Rev. Lett.
70
, 1895
–1899
(1993
).17.
D.
Bouwmeester
,
J.-W.
Pan
,
K.
Mattle
,
M.
Eibl
,
H.
Weinfurter
, and
A.
Zeilinger
, “
Experimental quantum teleportation
,” Nature
390
, 575
–579
(1997
).18.
D. H.
McIntyre
, Quantum Mechanics: A Paradigms Approach
(
Pearson Education Inc
.,
San Francisco
, 2012
).19.
N.
Gisin
,
G.
Ribordy
,
W.
Tittel
, and
H.
Zbinden
, “
Quantum cryptography
,” Rev. Mod. Phys.
74
, 145
–195
(2002
).20.
V.
Scarani
,
H.
Bechmann-Pasquinucci
,
N. J.
Cerf
,
M.
Dusek
,
N.
Lütkenhaus
, and
M.
Peev
, “
The security of practical quantum key distribution
,” Rev. Mod. Phys.
81
, 1301
–1350
(2009
).21.
H.-K.
Lo
,
M.
Curty
, and
K.
Tamaki
, “
Secure quantum key distribution
,” Nat. Photon.
8
, 595
–604
(2014
).22.
F.
Bouchard
,
K.
Heshami
,
D.
England
,
R.
Fickler
,
R. W.
Boyd
,
B.-G.
Englert
,
L. L.
Sánchez-Soto
, and
E.
Karimi
, “
Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons
,” Quantum
2
, 111
–123
(2018
).23.
X.-B.
Wang
, “
Beating the photon-number-splitting attacks in practical quantum cryptography
,” Phys. Rev. Lett.
94
, 230503
(2005
).24.
H.-K.
Lo
,
X.
Ma
, and
K.
Chen
, “
Decoy state quantum key distribution
,” Phys. Rev. Lett.
94
, 230504
(2005
).25.
T.
Kupko
,
M.
von Helversen
,
L.
Rickert
,
J.-H.
Schulze
,
A.
Strittmatter
,
M.
Gschrey
,
S.
Rodt
,
S.
Reitzenstein
, and
T.
Heindel
, “
Tools for the performance optimization of single-photon quantum key distribution
,” NPJ Quantum Inf.
6
, 29
(2020
).26.
C. H.
Bennett
and
G.
Brassard
, “
Quantum cryptography: Public key distribution and coin tossing
,” in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing
,
IEEE Press
,
Bangalore
, 1984
.27.
A.
Ekert
, “
Quantum cryptography based on Bell's theorem
,” Phys. Rev. Lett.
67
, 661
–663
(1991
).28.
P. G.
Kwiat
,
E.
Waks
,
A.
White
,
I.
Appelbaum
, and
P.
Eberhard
, “
Ultrabright source of polarization-entangled photons
,” Phys. Rev. A
60
, 773
–776
(1999
).29.
D.
Dehlinger
and
M.
Mitchell
, “
Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory
,” Am. J. Phys.
70
, 903
–910
(2002
).30.
R.
Rangarajan
,
M.
Goggin
, and
P.
Kwiat
, “
Optimizing type-I polarization-entangled photons
,” Opt. Express
17
, 18920
–18933
(2009
).31.
32.
D. S.
Naik
,
C. G.
Peterson
,
A. G.
White
,
A. J.
Berglund
, and
P. G.
Kwiat
, “
Entangled state quantum cryptography: Eavesdropping on the ekert protocol
,” Phys. Rev. Lett.
84
, 4733
–4736
(2000
).33.
E.
Toninelli
,
B.
Ndagano
,
A.
Vallés
,
B.
Sephton
,
I.
Nape
,
A.
Ambrosio
,
F.
Capasso
,
M. J.
Padgett
, and
A.
Forbes
, “
Concepts in quantum state tomographyand classical implementation with intense light: A tutorial
,” Adv. Opt. Photon.
11
, 67
–134
(2019
).34.
J. F.
Clauser
,
M. A.
Horne
,
A.
Shimony
, and
R. A.
Holt
, “
Proposed experiment to test local hidden-variable theories
,” Phys. Rev. Lett.
23
, 880
–884
(1969
).35.
J. A.
Carlson
,
M. D.
Olmstead
, and
M.
Beck
, “
Quantum mysteries tested: An experiment implementing Hardy's test of local realism
,” Am. J. Phys.
74
, 180
–186
(2006
).36.
D. F. V.
James
,
P. G.
Kwiat
,
W. J.
Munro
, and
A. G.
White
, “
Measurement of qubits
,” Phys. Rev. A
64
, 052312
(2001
).37.
J. B.
Altepeter
,
E. R.
Jeffrey
, and
P. G.
Kwiat
, “
Photonic state tomography
,” Adv. At. Mol. Phys.
52
, 105
–159
(2005
).38.
E. J.
Galvez
, “
Qubit quantum mechanics with correlated-photon experiments
,” Am. J. Phys.
78
, 510
–519
(2010
).39.
Kwiat Quantum Information Group,
“
Guide to Quantum State Tomography
” <http://research.physics.illinois.edu/QI/Photonics/Tomography/>© 2021 American Association of Physics Teachers.
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