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Comment by cromwellian | Hacker News Reader

This Google Talk https://www.youtube.com/watch?v=dEaecUuEqfc uses entanglement and quantum information theory in a clear and understandable way to explain 'spooky' quantum phenomena, like the quantum eraser, de-coherence, the aspect experiment, and the measurement problem. Even if you don't know any QM, just basic algebra and calculus, it's really approachable.

I used to be a fan of the Many Worlds interpretation, but after seeing this, I'm now a big fan of the Quantum Information Theory explanation. Starting about 43 minutes in, he goes into the QM Information Theory explanation, but I'd recommend watching the entire prezo.

Link to my original post on the subject: https://plus.google.com/110412141990454266397/posts/HC49S9ip...

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I'm having a difficult time following his explanation. Here are a few of my stumbling points. Maybe you can help me out.

1) What does it mean that entangled particles are supercorrelated? How can S(A|B) = 2 or -1?

2) The formula for Von Neumann entropy is S = -Tr(p log(p)), where p is the density matrix. How do you take a log of a matrix?

3) Why does the interpretation rely on the density matrix? I've always thought of the density matrix as something that gives information about our ignorance rather than the system (this is why the density matrix mixes classical probabilities in alongside quantum amplitudes/probabilities - observer uncertainty is classical). Therefore, to me, any good interpretation of quantum mechanics ought to work without density matrices.

Unfortunately his paper here (http://www.flownet.com/ron/QM.pdf) doens't seem to have significantly more information than his talk.

Thanks for any help you can offer.

Didn't watch but,

1. Super-correlation is entanglement.

2. Tr (ρ log_2 ρ ) = Σ_k of λ_k log2 λ_k where λ_k is the k-th eigenvalue of ρ. Sometimes the log2 is instead ln.

3. Density matrix indicates degree of entanglement. You can measure L or R polarized light but you have an entanglement of the two. Mind you that detecting a bell state without loopholes has, to my knowledge, never been done. A systems density matrix for a system can be measured statistically (Quantum tomography?).

Without reading the paper or watching the video.

> 1) What does it mean that entangled particles are supercorrelated? How can S(A|B) = 2 or -1?

The density matrix does not have the same properties of a joint probability distribution, so quantum entropy doesn't really have the same properties of classical entropy. [1]

> 2) The formula for Von Neumann entropy is S = -Tr(p log(p)), where p is the density matrix. How do you take a log of a matrix?

The log of a matrix is defined as the inverse of the matrix exponential. The matrix exponential can be defined as the usual power series, only using matrices rather than scalars.

What one usually does is: diagonalize the matrix (if possible), take the log of the eigenvalues and rotate again. Obviously taking the log of a matrix is a little trickier than the exponential because if you have negative or complex-valued eigenvalues you have to be a bit more careful.

[1] http://arxiv.org/abs/quant-ph/9610005

Thanks for the link - it's exactly what I needed!

Good answers. Just a small comment: quantum entropy is a generalization of classical entropy. In particular, if A and B are classically correlated, then S(A|B) has all the properties of a classical entropy (Shannon's, in this case), for instance, it is non-negative.

What does classically correlated mean? Is it different than quantum correlated? (Is this analogous to the difference between pure and mixed states?)

>I used to be a fan of the Many Worlds interpretation, but after seeing this, I'm now a big fan of the Quantum Information Theory explanation.

I know that both MWI and QIT interpret entanglement differently but I am not sure if I understand why one precludes the other (Your g+ post didn't help me much). Can you please point out exactly where the conflict lies, as they still seem compatible to me (perhaps with minor adjustments)?

I must say, I'm not sure what he even means by this "zero universe" business. Sure, the classical illusion is bust, but the wave function itself, as far as we know, is real, is it not?

While we're at throwing quantum explanation links, here is the Quantum Physics Sequence on Lesswrong: http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ I'd say the math is even simpler there, yet the explanation go deeper. It's a long read however.

Doesn't it depend on what it means for a theoretical construct to be "real" or not? Isn't "does it work" a better question?

Don't get confused by simple words such as "real". It means what it obviously mean in everyday life.

For instance, apples are real, and gravity is real. So when you drop an apple, what happens? It falls. Now what really, ultimately happens? It falls.

Once in Hawaii, at a meeting of philosophers sitting around a table discussing reality, several days passed and Suzuki said nothing. And finally the chairman said, "You've been silent all this time. Would you say something about reality." And Suzuki didn't say anything. I think he may have looked up. Finally the man said, "Well, is this table real?" And Suzuki said, "Yes." And then the man said, "In what sense is it real?" And Suzuki said, "In every sense."

Recently, there was a paper talking about this aspect of quantum theory - http://xxx.lanl.gov/abs/1111.3328 ... well, it was "recently" and fresh in my mind, but it appears to be back in 2011 :)

Whether the wave function is real depends on your answer to the question: is momentum real? You can't directly measure or observe momentum, you can't point to it in the world, but you can definitely feel its impact and it's a convenient measure for certain properties of objects. In that sense the wave function is just as real.

But you can argue both those things are not as real as e.g. extension, force and energy, which are much more readily available to our senses.

Can't I just weigh Galileo's cannon ball, then based on T from when I dropped it know its momentum?

I think the difference comes on moving past the macroscopic world: say I drop a uranium atom into Shroedinger's box - I can't calculate at time T whether the cat is alive.

Yes, you can calculate the momentum it had anywhere along the path while it dropped. Does being able to calculate some property make it real? If I take the square root of the momentum and call it the 'squish' of an object, is my 'squish' property then real?

If readers want to dive in and get to the point where "entanglement = time's arrow" becomes evident, the post would be that on "decoherence" [1]

[1] http://lesswrong.com/lw/pp/decoherence/

And the paper that the talk is based on:

http://www.flownet.com/ron/QM.pdf

You would probably enjoy Dr. Chris Adami's Reddit AMA:

http://www.reddit.com/r/science/comments/236ap1/science_ama_...

There seems to be a growing understanding that our universe is actually made of three things, not two: matter, energy, and information. Informatics is joining with thermodynamics and matter physics / chemistry as a fundamental science of "stuff."

It's important to capitalize the A in Aspect, as it refers to the name of the physicist.

http://en.wikipedia.org/wiki/Alain_Aspect

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