Observers

[arfa brane]

As far as entanglement and von Neumann entropy is concerned, if entanglement were as widespread as you suggest, . . .

It isn't me suggesting it but the likes of Susskind, Maldacena, and so on.

would you not expect that entropy effects from varying degrees of it should be visible in the measured entropy of macroscopic matter?

Entropy is a mysterious thing, fo' sho.

Can you list any of the differences between thermodynamic, and information entropy that might illuminate what von Neumann entropy is?

 

[exchemist]

It isn't me suggesting it but the likes of Susskind, Maldacena, and so on.
Entropy is a mysterious thing, fo' sho.

Can you list any of the differences between thermodynamic, and information entropy that might illuminate what von Neumann entropy is?

No, as I believe I said earlier, I know nothing about information entropy except that it should not be confused with thermodynamic entropy.

I had thought that von Neumann entropy was the same concept as thermodynamic entropy but extended to apply to individual QM systems which, not being ensembles at thermal equilibrium, would not meet the conditions for classical thermodynamic entropy to be defined. Do you think it is something different, then, such that it tells us nothing about the thermodynamic entropy of matter? Or are you just asking?

 

[The God]

It is quite obvious that the idea of Quantum Entanglement would have come from maths only, it could not have come from some kind of direct physical observation...(Ref EPR).

Now the straightforward question ....Do we have a QM expert here who can explain which part of QM maths or equations predict entanglement?~~~

 

[iceaura]

But you have prepared a state. So what difference is there between preparing a quantum state and measuring one?

When you prepare a state of entanglement, you deprive yourself of information about the properties of the particles involved. When you measure one of these properties, you obtain information about it.
When you create entanglement of your particle, it then exists in multiple states. When you make a measurement, it then exists in only one.
I'm having trouble imagining the similarity, rather than the differences.

Nonetheless, entangled states can persist, especially if the particles are photons propagating through empty space.

A floor being walked on is not an empty space.

 

[arfa brane]

When you prepare a state of entanglement, you deprive yourself of information about the properties of the particles involved.

In what way do you deprive yourself of information?
When you prepare entangled photons with SPDC, what don't you know about the emerging photons?

When you create entanglement of your particle, it then exists in multiple states.

No. An entangled state is a single state. If you have entangled a pair of photons, measuring one of them can give you information about the other without having to measure it.

 

[arfa brane]

I had thought that von Neumann entropy was the same concept as thermodynamic entropy

Well, no.
Understanding what Shannon entropy is might be helpful there. Information entropy and entanglement entropy are kind of the same thing, except one is classical.
Another difference between classical and quantum entropy is that the von Neumann measure is sodding useless with mixed states.
(so what?)

 

[arfa brane]

Hmm.

We . . . argue that the Von Neumann entropy quantifies the incompressible information content of the quantum source (in the case where the signal states are pure) much as the Shannon entropy quantifies the information content of a classical source.

 

[iceaura]

When you prepare entangled photons with SPDC, what don't you know about the emerging photons?

What their spin states are.

No. An entangled state is a single state.

It's a superposition of multiple states. At least, that's what they keep telling me, and running me through Bell's Theorem, and I can't see any way around it.

 

[arfa brane]

What their spin states are.

But you do know that measurement, if you do any, will show there are correlated spin states.
You don't know in advance what the measurements will be because you can't predict the future either (unlike with a Newtonian equation).

It's a superposition of multiple states.

Yes, but the superposition is not separable, you no longer have a bunch of pure states. Properly it's a product state.

We already have a logical model of entanglement: a pair of Bloch spheres, one of which is rotated into the Hadamard basis, are the inputs to a CNOT gate (really this is more like a tensor), which outputs the same pair in an entangled state. What gets entangled? A complementary degree of freedom, of course.

The Bloch spheres are qubits 'coordinatized' so that we have a map from SU(2) to a spherical system of coordinates. The degrees of freedom correspond to rotations, there is some character of complex numbers that make them "just right", the reals too large, and the quaternions too small, in this respect. Don't ask me.

 

[arfa brane]

Two photons are in a bar.

One says, "It's a good thing we're indistinguishable mate, or one of us could be bouncing off a wall right now."

(arf!)

 

[iceaura]

But you do know that measurement, if you do any, will show there are correlated spin states.

And destroy the entanglement. You have correlated spin states, or you have entanglement - one or the other, not both.

Yes, but the superposition is not separable, you no longer have a bunch of pure states. Properly it's a product state.

In which you lack information about the factor states - even if you had it before you entangled them. Hence the difference between measuring and entangling - your question, recall.

 

[exchemist]

It is quite obvious that the idea of Quantum Entanglement would have come from maths only, it could not have come from some kind of direct physical observation...(Ref EPR).

Now the straightforward question ....Do we have a QM expert here who can explain which part of QM maths or equations predict entanglement?~~~

Oh that's quite straight forward and not due to any special maths or equation but just a part of the whole concept of the wave function as a probability amplitude for a system. If you read about Schroedinger's Cat it should be obvious to you how it arises.

 

[exchemist]

But you do know that measurement, if you do any, will show there are correlated spin states.
You don't know in advance what the measurements will be because you can't predict the future either (unlike with a Newtonian equation).

Yes, but the superposition is not separable, you no longer have a bunch of pure states. Properly it's a product state.

We already have a logical model of entanglement: a pair of Bloch spheres, one of which is rotated into the Hadamard basis, are the inputs to a CNOT gate (really this is more like a tensor), which outputs the same pair in an entangled state. What gets entangled? A complementary degree of freedom, of course.

The Bloch spheres are qubits 'coordinatized' so that we have a map from SU(2) to a spherical system of coordinates. The degrees of freedom correspond to rotations, there is some character of complex numbers that make them "just right", the reals too large, and the quaternions too small, in this respect. Don't ask me.

This is word salad. How useless to pretend to explain something by dragging in a whole set of new and unexplained concepts and terms. Why don't we try to make this simple, instead of tangling it up in skeins of ever more esoteric gobbledegook?

Iceaura is perfectly right. An entangled state for the classic pair of particles is clearly a superposition of 2 states for the combined system, one of which has particle A spin up and B down, and the other has particle A down and B up. Obviously you can't define a state for one particle alone, because of the mutual dependence of the two, hence you work on a combined system state. Regarding that combined system state, you have in effect the Schroedinger's Cat situation (a mixture of up/down and down/up) until you measure one particle.

That's it, so far as I can see.

 

[arfa brane]

Iceaura is perfectly right. An entangled state for the classic pair of particles is clearly a superposition of 2 states for the combined system,

You can't really call it a superposition, that implies a linear combination of states and that you can still separate them.
If you don't know the photons are entangled, measuring one of them "destroys" the entangled information.

What I was trying to point towards, by interrogating iceaura's or your pov of the difference between preparation of entangled states and their measurement, is that it's about what you know: if you observe the preparation you can have information someone measuring one of the two particles doesn't have.
That's really it, as far as I can see.

So then, otherwise there is no difference between preparation and measurement (both are interactions) except what different observers might have to say.

p.s. the gobbledegook I posted is the kind of language you would use when programming a quantum computer.

 

[arfa brane]

I'll quote something posted at physicsforums about the subject

. . . it's perfectly sensible to talk about, say, the spin of a single particle becoming entangled with its angular momentum in spin-orbit coupling.
It's exactly the same phenomenon and that is the language widely used.

-- https://www.physicsforums.com/threads/how-to-entangle-two-particles.786810/

Preskill talks about radiation from an event horizon becoming entangled with a surface of constant time, not with particles.

 

[exchemist]

I'll quote something posted at physicsforums about the subject
-- https://www.physicsforums.com/threads/how-to-entangle-two-particles.786810/

Preskill talks about radiation from an event horizon becoming entangled with a surface of constant time, not with particles.

Yes I have now realised that you are using "entanglement" in a wide variety of contexts in which most physical scientists never would - or certainly never would have done when I was at university in the 1970s.

Spin-orbit coupling is a good example. One talks of the individual momenta ceasing to be "well-defined" and so forth. So instead of s and l you get j (in j-j coupling, that is), and so forth. I never, ever, heard anybody mention "entanglement" in such a context, throughout my 4 years at university. I can't see what dragging this term into such things adds to understanding. It just confuses and adds an unnecessary layer of mystique. It also strikes me as running the risk of degrading the term, so that it loses its meaning in the special contexts in which is useful, namely when you have correlated QM entities separated on a macroscopic scale.

But at least you and I are now on the same page, to the extent that I realise when you say "entanglement" you include any QM phenomenon in which the properties of individual QM entities are no longer well-defined. Just don't expect me to agree to start using it in such a sweeping way.

 

[arfa brane]

I can't see what dragging this term into such things adds to understanding. It just confuses and adds an unnecessary layer of mystique. It also strikes me as running the risk of degrading the term, so that it loses its meaning in the special contexts in which is useful, namely when you have correlated QM entities separated on a macroscopic scale.

I admit I had the same misgivings some time ago. But these as it turns out, were misplaced--entanglement is very general, you don't even need particles: (from the same physicsforum poster)

Given that, again, there's no need for the things being entangled to even be particles, there's no fundamental relationship between entanglement and conservation [of energy].
Generally, the physical processes that mediate interactions between different degrees of freedom have certain conservation laws associated with them, but that's completely general and nothing to do with entanglement.

What do you think of the last sentence, why does he say conservation laws have nothing to do with entanglement?

p.s. apart from needing a woo umbrella, I don't think it's all that embarrassing to have to admit there's something about QM (as a theory of quantum probabilities) you thought you understood but didn't. The unreasonableness of it all appears to confound even very educated (and presumably intelligent) people, you're not alone.

 

[exchemist]

I admit I had the same misgivings some time ago. But these as it turns out, were misplaced--entanglement is very general, you don't even need particles: (from the same physicsforum poster)

What do you think of the last sentence, why does he say conservation laws have nothing to do with entanglement?

p.s. apart from needing a woo umbrella, I don't think it's all that embarrassing to have to admit there's something about QM (as a theory of quantum probabilities) you thought you understood but didn't. The unreasonableness of it all appears to confound even very educated (and presumably intelligent) people, you're not alone.

That's exactly what I mean.

Here we have a perfectly well understood phenomenon like spin-orbit coupling, taught to all chemistry undergrads. But now, you give it the label "entanglement" - and promptly claim that I no longer understand it! All that has changed is your terminology.

 

[arfa brane]

I'm not claiming you don't understand spin-orbit coupling, but I have to say there is evidence you and others here have some common misconceptions about what entanglement is.

As to what it means, I think that's a question with a different character altogether.
I also think that the entropy measure, von Neumann's measure, not being useful with entangled or mixed states, plus the fact that finding an entropy measure for them is hard is something significant. Significant how I'm not too sure, but quantum information theory could tell me something.

But yes, it's perhaps surprising that entanglement isn't necessarily between particles, or about conservation of say, momentum.

 

[exchemist]

I'm not claiming you don't understand spin-orbit coupling, but I have to say there is evidence you and others here have some common misconceptions about what entanglement is.

As to what it means, I think that's a question with a different character altogether.
I also think that the entropy measure, von Neumann's measure, not being useful with entangled or mixed states, plus the fact that finding an entropy measure for them is hard is something significant. Significant how I'm not too sure, but quantum information theory could tell me something.

But yes, it's perhaps surprising that entanglement isn't necessarily between particles, or about conservation of say, momentum.

No but this is a real point about what entanglement is and I see little evidence that you understand it yourself, though I certainly admire the extensiveness of your reading. I don't want you sliding off into other assertions until we dig down a bit on this.

You claim that spin-orbit coupling is a manifestation of entanglement. Now I got taught about that by means of things like perturbation theory, whereby a notional one-electron state is perturbed by the influence of others, resulting in states that are not simply those of one electron systems but mixtures. You, apparently, choose to call that "entanglement". But can you tell me what it is you can measure about spin-orbit coupling that instantly reveals the value of some other quantity correlated with it? If not, what is the point of describing spin-orbit interactions as "entanglement"?

I am resisting this all-embracing usage of entanglement you are promoting because it strikes me as unhelpful, glib and obscurantist. It seems to try to make something we understand mysterious again. That is not what science ought to do. Mixing of states, in various contexts, is bread and butter for the quantum chemist, not least to explain chemical bonding. We never called that entanglement and I am glad we didn't.

Please, if you are convinced that the concept of entanglement provides useful insights into the nature of spin-orbit coupling, show me how you demonstrate its utility in this context. And then, if it can be applied to chemical bonding, I'd like to have a think about that as well.