
Quantum Randomness - Tomte
http://www.americanscientist.org/issues/id.16217,y.2014,no.4,content.true,page.1,css.print/issue.aspx
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md224
Enjoyed the shout-out to Bohmian mechanics. Nonlocality may be weird, but you
know what else is weird? _Everything else about quantum mechanics._ I'd
actually prefer a nonlocal deterministic theory to a local indeterministic
one, though I know that's just a philosophical preference. Still, I wish
Bohmian mechanics was more popular; I wasn't even aware it existed until
recently.

~~~
TTPrograms
Multiverse is perfectly deterministic without all the issues with Bell's
Inequality and needing a superfluous particle in addition to the wavefunction.
I think pilot wave is throwing the baby out with the bathwater.

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cromwellian
Pure randomness doesn't need physicality. The expansion of Omega, Chaitin's
constant, is random. There is no model, program, or equation, that can predict
the next bit.

Perhaps its possible the universe could be run on a cellular automata that is
unpredictable in the same way. Is say, radioactive decay, truly random, or
just can't be predicted by any program shorter than the underlying cellular
automata process itself.

The fact that we can model the universe at all and predict parts of it at
various scales -- that math works at all for physics -- is either remarkable,
or perhaps required in any universe capable of intelligent life. :) Perhaps in
a universe that is incomprehensible otherwise, evolution would not select for
intelligence.

~~~
darkmighty
That's referenced in the article -- Chaitin's constant is 'algorithmically
incompressible' according to Kolmogorov complexity -- though note that this
definition means it's "assymptotically" random, but the first n bits can be
approximated in finite time (there are other numbers with more strict
randomness). What the article addresses is that if you're given a long string
with that property you can't verify the randomness, by definition. But using
the CHSH method outlined you can, assuming only some physical principles --
provided you're given a small 'seed' to start.

Note that the underlying "way" that the universe generates randomness doesn't
matter from a scientific standpoint -- as long as we can't predict it, you can
think of it as being generated by either an enormous computer or truly random
(whatever that means).

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dj-wonk
About 3/4 of the way down, in response to: "The central idea in all of these
protocols is simply to be stingy with the use of randomness. We ask Alice and
Bob to play the CHSH game over and over again. However, in almost all of the
plays, they simply both receive red cards—leading to a boring but also “cheap”
(in terms of randomness) game. Only for a few randomly chosen plays does one
of them receive a blue card."

If this is true, then these "clever" protocols are breaking the 50/50 rule of
the CHSH game. Right?

~~~
greeneggs
Yes. In the normal CHSH game, the questions to the players Alice and Bob are
independent random bits (50/50, as you say). That's a problem, though, if you
want to create new randomness, because you put into the game two random bits
and you get out less than two random bits! If you want to get out more
randomness than you put in, you need to be a little more clever and more
stingy with using random bits.

(If the players are honest, the first player's output is uniformly random, but
the second player's output is ~85% predictable given the first player's
output. Measured in terms of entropy, this means you are getting a fraction
more than 1 bit out.)

The standard 50/50 CHSH is still useful for generating randomness, though.
Even though it uses up more randomness than it creates, the output randomness
can be of higher _quality_ than the input randomness. More precisely, if the
input bits are independent to the players Alice and Bob, but perhaps are known
to an outside adversary, the game's output bits will be unknown to the
adversary.

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xtacy
It is interesting to see how outcomes of the CHSH game to generate random
bits. However, I am left wondering how Alice, Bob, or an external observer
learns about the outcomes of the game?

Or, maybe I am misunderstanding the mechanics itself.

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trurl42
The idea of infinite randomness expansion really fascinates me, it's like
watching Münchhausen pulling himself out of the swamp by his own hair.

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sundaymorning
How exactly do Alice and Bob use entangled electrons to win CHSH game with
higher than 75% probability?

~~~
dj-wonk
This may not answer your question, but you might enjoy seeing how the 85.4%
probability is derived in
[http://arxiv.org/pdf/1209.0448v1.pdf](http://arxiv.org/pdf/1209.0448v1.pdf)
and
[http://arxiv.org/pdf/1209.0449v1.pdf](http://arxiv.org/pdf/1209.0449v1.pdf)

~~~
Sniffnoy
A note -- if you're linking to arXiv, it's better to link to the abstract
([http://arxiv.org/abs/1209.0448](http://arxiv.org/abs/1209.0448),
[http://arxiv.org/abs/1209.0449](http://arxiv.org/abs/1209.0449)) rather than
directly to the PDF. From the abstract, one can easily click through to the
PDF; not so the reverse. And the abstract allows one to do things like see
different versions of the paper, search for other things by the same authors,
etc.

