Quantum entanglement is a phenomenon that has no classical counterpart; it is not only difficult to learn but also difficult to teach. It is often an omitted or underrepresented topic in the syllabus of an introductory quantum mechanics or modern physics course. Nearly 40 years ago Mermin published a thought experiment to analyze a device consisting of a transmitter and two receivers. The receivers each had a three-position switch and two lights, one red and one green. Analysis of the operation of the device follows the predictions of quantum mechanics but only simple mathematics is employed to demonstrate the peculiar nature of quantum entanglement. A few years later he reintroduced his quantum device to a more general audience in a Physics Today article and provided another interesting interpretation. In the current paper, we make use of the recently published work in quantum information theory by Candela to have students write code to simulate the operation of the device in that article. Analysis of the device has significant pedagogical value—a fact recognized by Feynman—and simulation of its operation provides students a unique window into quantum mechanics without prior knowledge of the theory.

1.
See the “Theme issue: The intersection of biology and physics,”
Am. J. Phys
82
(
5
),
365
366
(
2014
) and associated articles.
2.
J.
Bernstein
,
P.
Fishbane
, and
S.
Gasiorowicz
,
Modern Physics
(
Prentice
-
Hall Inc
.,
Upper Saddle River, NJ
,
2000
).
3.
R.
Harris
,
Nonclassical Physics: Beyond Newton's View
(
Addison-Wesley
,
Menlo Park, CA
,
1999
).
4.
P.
Tipler
and
R.
Llewellyn
,
Modern Physics
, 6th ed. (
W.H. Freeman and Co
.,
New York, NY
,
2012
).
5.
R.
Riedinger
 et al., “
Remote quantum entanglement between two micromechanical oscillators
,”
Nature
556
,
473
477
(
2018
).
6.
D. V.
Schroeder
, “
Entanglement isn't just for spin
,”
Am. J. Phys
85
(
11
),
812
820
(
2017
).
7.
F. W.
Strauch
, “
Resource Letter QI-1: Quantum Information
,”
Am. J. Phys.
84
(
7
),
495
507
(
2016
).
8.
N. D.
Mermin
, “
Bringing home the atomic world; Quantum mysteries for anybody
,”
Am. J. Phys.
49
(
10
),
940
943
(
1981
).
9.
matlab
, The MathWorks, Inc.,
Natick
,
MA
.
10.
A.
Einstein
,
B.
Podolsky
, and
N.
Rosen
, “
Can quantum mechanical description of physical reality be considered complete?
,”
Phys. Rev.
47
,
770
780
(
1935
).
11.

In the video(s), Feynman discusses a device somewhat different with buttons and such. He does credit the original idea to Mermin. From youtube.com, <https://www.youtube.com/watch?v=AyejXtZrGb0>, the description reads, “Richard Feynman discusses Quantum Mechanics in a workshop at the Esalen Institute, Big Sur, CA. 1983. Topics are: Heisenberg's uncertainty principle, Bell's theorem and the Einstein-Podolsky-Rosen paradox.”

12.
N. D.
Mermin
, “
Is the moon there when nobody looks? Reality and the quantum theory
,”
Phys. Today
38
(
4
),
38
(
1985
).
13.
P. A. M.
Dirac
, “
A new notation for quantum mechanics
,”
Math. Proc. Cambridge Philos. Soc.
35
(
3
),
416
418
(
1939
).
14.
P. A. M.
Dirac
,
The Principles of Quantum Mechanics
, 4th ed. (
Oxford U. P.
,
New York
,
1958
), pp.
16
22
.
15.
N. D.
Mermin
, “
From Cbits to Qbits: Teaching computer scientists quantum mechanics
,”
Am. J. Phys.
71
(
1
),
23
30
(
2003
).
16.
D.
Candela
, “
Undergraduate computational physics projects on quantum computing
,”
Am. J. Phys.
83
(
8
),
688
702
(
2015
).
17.
See supplementary material at http://dx.doi.org/10.1119/10.0000833 for the matlab code.
18.

If the complex amplitudes have subscripts beginning with zero such as a0,a1,a2,a3 corresponding to |00,|01,|10,|11, then the subscript is the decimal representation of the binary number inside the bracket.

19.
J.
Sakauri
,
Advanced Quantum Mechanics
(
Addison-Wesley
,
Reading, MA
,
1967
), 9th printing (1982), pp
225
226
.
20.

This convention is different from that in Ref. 8. In that publication, Mermin has one detector flash red if the spin is up and the other flash green if the spin is up. He uses a spin-singlet state of the form 12(|01|10), which is antisymmetric to the exchange of the two particles. In this simulation, each detector flashes red for |0 and green for |1. In addition, the entangled Bell state that is generated is 12(|00+|11).

21.
D. V.
Schroeder
and
T. A.
Moore
, “
A computer-simulated Stern-Gerlach laboratory
,”
Am. J. Phys.
61
(
9
),
798
805
(
1993
).

Supplementary Material

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