

How Quantum Pairs Stitch Space-Time - digital55
https://www.quantamagazine.org/20150428-how-quantum-pairs-stitch-space-time/

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jrapdx3
The Escher work used as illustration (re: Demons, et. al.) has a decidedly
fractal look about it, which prompts the thought that the entanglement
described in the article could be understood as a multidimensional fractal.

Kind of like the way polymerization of organic molecules occurs in specific
ways and produces shaped structures accordingly, entangled particles build
space-time shapes depending on patterns of entanglement, and perhaps not
necessarily always the same pattern, leaving unevenness of space-time shape.

Just musing about the significance of the idea. It certainly has a lot of
intuitive appeal.

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geoelectric
_Even if your lump of gold has just 100 atoms, each with a quantum “spin” that
can be either up or down, the total number of possible states totals 2[^]100,
or a million trillion trillion. With every added atom the problem grows
exponentially worse. (And worse still if you care to describe anything in
addition to the atomic spins, which any realistic model would.) “If you take
the entire visible universe and fill it up with our best storage material, the
best hard drive money can buy, you could only store the state of about 300
spins,” said Swingle. “So this information is there, but it’s not all
physical. No one has ever measured all these numbers.”_

I realize this is likely a translation error, but the amount of space required
to keep the state of 300 up/down spins is 300 bits, or 38 bytes.

Now, the space to keep all possible states of 300 spins, that's different.
That's what lazy evaluation (and a lot of time on your hands!) is for.

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danbruc
The article is actually correct - the general state of a system of 300 spins
is described by 2^300 complex amplitudes. The remaining question is how much
memory you are willing to spend per amplitude but with two doubles it will
take 2.6 * 10^92 bits. You only get away with 300 amplitudes if the spins are
not entangled and the state of the system therefore is a product state, i.e.
you can factor the state of the system into 300 independent states, one per
spin.

A two spin system for example has the general state

    
    
      a |DD> + b |DU> + c |UD> + d |UU>
    

requiring four complex amplitudes, not two bits only selecting one of the
basis states.

EDIT: Could not resist. The storage density of a 15 mm thick 2 TB 2.5" hard
disk is 152.7 Ebit/m³. With the number from above this yields 2 * 10^27 ly³
for the volume which is not to far from the visible universe with 4 * 10^32
ly³ according to Wikipedia. Okay, it is a factor of 200,000 but that will only
buy you 17 more bits plus some space for cable routing.

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Retric
This seems like a clasic analog issue. Does adding 1 spin to a 300 spin system
add _exactly_ 2^300 bits of information and 1 spin to a 2 spin situation
_exactly_ 2^2 = 4 bits of information?

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bkcooper
As mentioned elsewhere, bits are probably the wrong way to think about it.
Does it really double the size of your Hilbert space? Yes.

Perhaps this will help clarify why it is different. In the classical case,
adding one more spin is doubling the size of your set. In the quantum
mechanical case, adding one more spin instead doubles the dimensionality of
the space of possible states.

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Slackwise
Been recently studying Lisp/Scheme, and I couldn't help but relate these
"Quantum Pairs" with cons cells and the relationship described as a tree data
structure. (Not equating them here, just a musing of mine.)

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idbentley
It's analogies all the way down.

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eli_gottlieb
The use of Lies to Children in scientific and mathematical writing tends to
send me scurrying to Wikipedia to look up what's really going on, yeah.

