The celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Found. Phys. 1, 23–33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park's demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning.
References
1.
M. A.
Nielsen
and I. L.
Chuang
, Quantum Computation and Quantum Information
, 10th Anniversary Edition (Cambridge U.P.
, Cambridge
, 2016
).2.
N.
David Mermin
, Quantum Computer Science
(Cambridge U.P.
, New York
, 2007
).3.
W. K.
Wootters
and W. H.
Zurek
, “A single quantum cannot be cloned
,” Nature
299
, 802
–803
(1982
).4.
D.
Dieks
, “Communication by EPR devices
,” Phys. Lett. A
92
, 271
–272
(1982
).5.
P. W.
Milonni
and M. L.
Hardies
, “Photons cannot always be replicated
,” Phys. Lett. A
92
, 321
–322
(1982
).6.
Wikipedia
<https://en.wikipedia.org/wiki/Asher_Peres>7.
A.
Peres
, “How the no-cloning theorem got its name
,” Forts. Phys.
51
, 458
–461
(2003
).8.
N.
Herbert
, “FLASH-A superluminal communicator based upon a new kind of quantum measurement
,” Found. Phys.
12
, 1171
–1179
(1982
).9.
Wikipedia
<https://en.wikipedia.org/wiki/Esalen_Institute>10.
V.
Scarani
, S.
Iblisdir
, N.
Gisin
, and A.
Acín
, “Quantum cloning
,” Rev. Mod. Phys.
77
, 1225
–1256
(2005
).11.
J. L.
Park
, “The concept of transition in quantum mechanics
,” Found. Phys.
1
, 23
–33
(1970
).12.
Shtetl-optimized
<https://www.scottaaronson.com/blog/?p=2903/>.13.
S.
Wiesner
, “Conjugate coding
,” ACM SIGACT News
15
, 78
–88
(1983
).14.
A.
Zeilinger
, “Light for the quantum. Entangled photons and their applications: A very personal perspective
,” Phys. Scr.
92
, 072501
(2017
).15.
Web of Science
<https://aps.webofknowledge.com/>16.
<https://citations.springer.com/item?doi=10.1007/BF00708652> for a list of the citations to Park's paper.
17.
18.
E.
Farhi
and A.
Harrow
, “Quantum cloning quantum money and quantum monogamy
,” Physics@MIT
58
–66
(2013
).19.
A.
Einstein
, B.
Podolsky
, and N.
Rosen
, “Can quantum-mechanical description of physical reality be considered complete?
,” Phys. Rev.
47
, 777
–780
(1935
).20.
D.
Kaiser
, How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival
(W.W. Norton, Inc.
, New York
, 2011
).21.
J. L.
Park
and H.
Margenau
, “Simultaneous measurability in quantum theory
,” Int. J. Theor. Phys.
1
, 211
–283
(1968
).22.
J. L.
Park
, “Quantum theoretical concepts of measurement: Part I
,” Philos. Sci.
35
, 205
–231
(1968
).23.
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
).24.
A.
Peres
, “Neumark's theorem and quantum inseparability
,” Found. Phys.
20
, 1441
–1453
(1990
).25.
C. H.
Bennett
and P. W.
Shor
, “Quantum information theory
,” IEEE Trans. Inf. Theory
44
, 2724
–2742
(1998
).26.
D. N.
Mermin
, “What's wrong with this pillow?
,” Phys. Today
42
(1
), 9
–10
(1989
).27.
C. H.
Bennet
, “Quantum information and computation
,” Phys. Today
48
(10
), 24
–30
(1995
).28.
D.
Bouwmeester
, J. W.
Pan
, K.
Mattle
, M.
Eibl
, H.
Weinfurter
, and A.
Zeilinger
, “Experimental quantum teleportation
,” Nature
390
, 575
–579
(1997
).29.
V.
Buzek
and M.
Hillery
, “Quantum copying: beyond the no-cloning theorem
,” Phys. Rev. A
54
, 1844
–1852
(1996
).© 2018 American Association of Physics Teachers.
2018
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
