1. Quantum Computer Science: A Very Short Introduction (3)

2. Nobel Prize in Physics (1979)
Steven Weinberg
(born: 1933)
Nobel Prize in Physics (1979)

3. (The New York Review of Books,
We naturally tend to think that reality can be described locally. I can say what is happening in my laboratory, and you can say what is happening in yours, but we don’t have to talk about both at the same time. But in quantum mechanics it is possible for a system to be in an entangled state that involves correlations between parts of the system that are arbitrarily far apart, like the two ends of a very long rigid stick.
For instance, suppose we have a pair of electrons whose total spin in any direction is zero. In such a state, the wave function (ignoring everything but spin) is a sum of two terms: in one term, electron A has positive spin and electron B has negative spin in, say, the north direction, while in the other term in the wave function the positive and negative signs are reversed. The electron spins are said to be entangled. If nothing is done to interfere with these spins, this entangled state will persist even if the electrons fly apart to a great distance. However far apart they are, we can only talk about the wave function of the two electrons, not of each separately. Entanglement contributed to Einstein’s distrust of quantum mechanics as much or more than the appearance of probabilities.
Strange as it is, the entanglement entailed by quantum mechanics is actually observed experimentally. But how can something so nonlocal represent reality?
The Trouble with
Quantum Mechanics by
Steven Weinberg
(The New York Review of Books,
January 19, 2017)

4. N. David Mermin, Quantum Computer Science – An Introduction
Such an argument for elements of reality – predetermined values – was put
forth in 1935 (in a different context) by Albert Einstein, Boris Podolski, and
Nathan Rosen (EPR). The controversy and discussion it has given rise to has
steadily increased over the past seven decades. The terms “incomplete” and
“element of reality” originated with EPR. Today it is Einstein’s most cited
paper.
N. David Mermin, Quantum Computer Science – An Introduction
(New York: Cambridge University Press, 2007, page 157)

5. EPR and the Bell inequality

7. Charlie
Alice
Bob

18. Spooky actions at a distance: Mermin’s mysterious device

19. Three unconnected parts
The device:
Three unconnected parts
Detector A
Source C
Detector B

20. Detector A

21. Mermin’s device

29. Bell’s inequality tells us that regardless of how the instruction sets are
distributed, in all runs of the experiment the same color must flash 55.5% of the
time. But as the device actually operates, the same color flashes 50% of the time.
The device violates Bell’s inequality. But Bell’s inequality is a consequence of
the existence of instruction sets. Therefore instruction sets cannot exist.
But instruction sets were the only explanation we were able to find for how lights
can flash the same color when the switches had the same setting. So, how can
they? Yet they do. That is the conundrum posed by the device – its sublime
mystery.
N. David Mermin, Boojums All The Way Through (pages 143 – 144).
New York: Cambrige University Press, 1990.

30. The physics behind Mermin’s device – 1

31. The physics behind Mermin’s device – 2

32. The physics behind Mermin’s device – 3
The lights always flash the same color
when the switches have the same setting
because the detectors are then measuing
the polarization of the two photons along
the same direction.
Postulate 1

33. The physics behind Mermin’s device – 4
The same color flashes as often as different
ones. The switches have one of the settings:
12, 13, 21, 23, 31, or 32. Hence, the two
disks will be at 60° to one another. So, the
polarizations will be the same 25% of the
time:
cos(60°) = (1∕2) 2 = 1 4 .
But then:
6 9 ×25%+ 3 9 ×100%= = 1 2 =50%
Postulate 2