Observers

[exchemist]

And since entanglement, say the production of maximally entangled photons, does involve interaction, then why is any interaction not the cause of some amount of entanglement, even a very weak kind? Can you say you know the answer?

I see you added this after I had started to reply to your post as originally made, so here is a reply to the last bit.

Firstly, production of entangled photons is a rare and unusual process. Most photons are produced singly, not in pairs with opposite spin. Examples would be the emission of photons by atoms or molecules in excited states or by black body radiation - phenomena we see all around us daily. Do we need to invoke entanglement to account for this sort of thing? I can't see why.

Secondly, consider a simple, very common interaction related to the above, namely the absorption of a photon. It gets absorbed and promotes an electron to a higher energy orbital, with a different quantum of angular momentum, due to the spin of the absorbed photon. There is no entanglement of anything here.

Or consider a collision between two noble gas atoms, i.e. the simplest radiationless molecular interaction that is possible. Electrostatic repulsion deforms the outermost shell of electrons as the atoms approach, raising their energy as kinetic energy is lost and eventually the motion reverses and the atoms rebound apart, the energy of the deformed electron clouds being re-converted into kinetic energy again. No "entanglement" here either, so far as I can see.

And what is "weak" entanglement , as opposed to "maximal" entanglement? I had always thought either you knew the spin of the pair of photons or you didn't. How can you half-know?

 

[arfa brane]

Firstly, production of entangled photons is a rare and unusual process.

That isn't true, actually. Photons from opposite sides of a celestial object are entangled, as the Hanbury Brown and Twiss effect shows.

In the 1950's Hanbury Brown and Twiss showed that one could measure the angular sizes of astronomical radio sources and stars from correlations of signal intensities, rather than amplitudes, in independent detectors. Their subsequent correlation experiments demonstrating quantum bunching of photons in incoherent light beams were seminal in the development of quantum optics.

--https://arxiv.org/abs/nucl-th/9804026
https://arxiv.org/abs/nucl-th/9804026
When you use a non-linear crystal in SPDC, most of the photons are transmitted, only a small fraction are downconverted. Nonetheless, all the photons in the pump beam interact with the crystal. You also have to bear in mind, the pump beam is from a lasing medium, an ensemble of atoms interacting synchronously.

Ed. On the other hand, quantum computation is still around the corner because entangled states need to be stable, usually this is to do with how isolated the qubits are. And since photons are stable unless they interact with matter, they're more or less isolated in a vacuum.

 

[exchemist]

That isn't true, actually. Photons from opposite sides of a celestial object are entangled, as the Hanbury Brown and Twiss effect shows.

--https://arxiv.org/abs/nucl-th/9804026
When you use a non-linear crystal in SPDC, most of the photons are transmitted, only a small fraction are downconverted. Nonetheless, all the photons in the pump beam interact with the crystal. You also have to bear in mind, the pump beam is from a lasing medium, an ensemble of atoms interacting synchronously.

Ed. On the other hand, quantum computation is still around the corner because entangled states need to be stable, usually this is to do with how isolated the qubits are. And since photons are stable unless they interact with matter, they're more or less isolated in a vacuum.

I certainly did not know about HBT interferometry and I'll need to speed time reading the paper. And yes light in lasers is correlated due to emission being due to the usual stimulated emission process, i.e. the inverse of the absorption process, but you'll have to explain to me how entanglement is involved in any of this.

But before we get into your new counterexamples, what about my examples? How do you see entanglement arising in those?

 

[Write4U]

Oh what a tangled web we weave....

 

[exchemist]

Oh what a tangled web we weave....

Haha, but don't worry, nobody is practising to deceive here. We are trying to get to a common understanding of physics.

 

[Write4U]

The problem seems to be in the exchange of information when a separated entangled pair undergoes a change.

I recall Einstein's first response was an analogy of a pair of gloves. If one observer has a left handed glove, the other observer must have the right handed one, regardless where he is in the universe.
He later dropped this analogy, because if I take the left handed glove and turn it inside out, would the right handed glove magically also turn inside out?

It seems to me the main problem is not in the entanglement itself, but in the observation of any change.

IMO, any analogy to explain the phenomenon by any comparison to the physical world is inadequate. If there is such a thing as entanglement, it seems to me that this "correlation" should be pursued at a different level, perhaps in context of a universal potential, such as Bohm's Implicate order.

 

[exchemist]

I certainly did not know about HBT interferometry and I'll need to speed time reading the paper. And yes light in lasers is correlated due to emission being due to the usual stimulated emission process, i.e. the inverse of the absorption process, but you'll have to explain to me how entanglement is involved in any of this.

But before we get into your new counterexamples, what about my examples? How do you see entanglement arising in those?

By the way, I've now read the paper. It seems to be about photon bunching, a property - so I now read- of boson statistics. Entanglement is nowhere mentioned, so if you are saying photon bunching is due to entanglement, again I'm afraid you will need to explain why this should be.

 

[arfa brane]

Entanglement.

It is something that appears to need at least a pair of "quantum systems".
The systems have to interact either by being close to each other, or by exchanging a photon (perhaps both).
Because they interact, the final state will be a product of both initial states. It's called a product state.
Factoring a product state is not possible if the systems are entangled.
Entanglement is largely about distinguishability . . .

In laboratory experiments, entanglement needs to be protected from the environment, this in no way can imply that entanglement (and its decoherence) doesn't occur all the time in any kind of quantum system.

As to the HBT effect, how does photon bunching give angular sizes of distant stars? How is it the correlations are not because of entanglement?

It is a bit frustrating; there is a lot of discussion about what entangled states are, but not a whole lot about how they occur in the first place.

 

[arfa brane]

It is very easy to create entangled systems. This happens all around us all the time. What is very hard is to have a controlled experiment where you as an experimenter control the entanglement, keep the system in the entangled state of your choice for a long [enough] time.

The wave function of one particle is capable of entangling with the wave of another particle it comes in contact with. Such entanglements are usually weak and have only a neglegible impact on a particle's measured properties. An example is the weak entanglement between photons in a beam of sunlight streaming through the window into my living room.

But if 2 particles are created at the same instant from the same source, for example conversion of a single unpolarized photon into 2 polarized photons by using a non linear crystal. These 2 photons are strongly entangled with respect to polarization.

Mr Sood appears to be implying that the degree of entanglement (up to maximal) depends on the interaction being localised in time and space--a maximal "overlap" perhaps.

 

[The God]

Two Photons/particles are given, is there any means to know that they are entangled?

If we create entangled Photons and track them, that will be kind of observation/measurement.

Degree of entanglement like strong or weak appears to be an unnecessary classical approach, it's either entangled or not.

 

[arfa brane]

Entanglement is a general property that [the] states [of] tensor product spaces may have (with respect to [a] particular factorization); any collection of independent degrees of freedom can be entangled together. That tensor product can be between any two Hilbert spaces, not just those corresponding to separate particles.

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

Two Photons/particles are given, is there any means to know that they are entangled?

The $64,000 question! No, unless you measure both photons somehow, then compare the results.
The individual meaurements can't distinguish any entanglement; the comparison is required.
However, if you know both photons were produced such that they are entangled, you don't need to do any measurements (obviously, since in fact you already have).

If we create entangled Photons and track them, that will be kind of observation/measurement.

What do you mean "track them"? Please explain.

Degree of entanglement like strong or weak appears to be an unnecessary classical approach, it's either entangled or not.

I refer you to von Neumann entropy.

The plot of von Neumann entropy (vertical) Vs Eigenvalue (horizontal) for
a bipartite 2-level pure state. When the eigenvalue has value .5, von Neumann
entropy is at a maximum, corresponding to maximum entanglement.

--https://en.wikipedia.org/wiki/Quantum_entanglement​

 

[iceaura]

However, if you know both photons were produced such that they are entangled, you don't need to do any measurements (obviously, since in fact you already have).

You haven't done any measurements. If/when you measure, you destroy the entanglement.

In laboratory experiments, entanglement needs to be protected from the environment, this in no way can imply that entanglement (and its decoherence) doesn't occur all the time in any kind of quantum system.

And is destroyed as soon as interaction with an "environment" - such as a measuring device, or other electrons in a given molecule, etc - takes place.

 

[arfa brane]

You haven't done any measurements. If/when you measure, you destroy the entanglement.

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

And is destroyed as soon as interaction with an "environment" - such as a measuring device, or other electrons in a given molecule, etc - takes place.

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

I have a question someone might be able to answer. Are the intensity correlations in HBT interferometry an entanglement measure? If not, why not?

 

[exchemist]

But you have prepared a state. So what difference is there between preparing a quantum state and measuring one?
Nonetheless, entangled states can persist, especially if the particles are photons propagating through empty space.

I have a question someone might be able to answer. Are the intensity correlations in HBT interferometry an entanglement measure? If not, why not?

It seems to me it is the "persisting" that is important here. From what I have read, it seems to me the normal usage of the term "entanglement" is restricted to those instances in which a pair of QM entities remain described by a single combined state function, embracing a range of measurement outcomes, at long range, until one is determined, whereupon the other is also determined. It is the long range that gives rise to all the speculation about spooky action at a distance and all that.

If an atom emits a photon, I suppose it must be the case that so long as the orientation of spin of the photon is not determined, it is best described by a superposition of states which is linked to the (similarly undetermined) orientation of the corresponding change in angular momentum of the emitting atom. So they are "entangled" in the sense that you can describe them as a linked pair, in which determination of one automatically determines the other, until one of them interacts with something else. But this seems to me trivialising the term "entanglement" as it leads to no insight and no special phenomena (or not so far as I can see). It is no more than Schroedinger's Cat, really: an amusing way in which you can choose to describe the world, but which does not get you anywhere.

The HBT thing, on the other hand, seems to be an instance of photon bunching, occurring in a situation in which the source is at long range from the detector. Rather like the double slit experiment, the phenomenon is predicted from non-QM classical wave theory and only becomes problematic when a particle view of it is considered. I can see what you mean (vaguely) , in that there is an apparent issue about how the emitter "knows" to emit photons so that they tend to arrive at the detectors in bunches. But again this seems to me distinct from what I would call proper entanglement, as I can't quite see how there is anything in this case where determination of the state of one entity automatically allows the state of the other to be known. It is mysterious, just as the double slit experiment is mysterious, but just as the double slit experiment is not entanglement, I don't - so far - see why this would be.

Perhaps you can explain why you think it is.

And, to go back to the original assertion of yours that all interaction creates entanglement, I still do not buy that at all, based on the examples I gave (and which you have yet to address). I would also welcome an explanation of what is meant by "weak", or "maximal", entanglement.

 

[exchemist]

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

The $64,000 question! No, unless you measure both photons somehow, then compare the results.
The individual meaurements can't distinguish any entanglement; the comparison is required.
However, if you know both photons were produced such that they are entangled, you don't need to do any measurements (obviously, since in fact you already have).

What do you mean "track them"? Please explain.I refer you to von Neumann entropy.

The plot of von Neumann entropy (vertical) Vs Eigenvalue (horizontal) for
a bipartite 2-level pure state. When the eigenvalue has value .5, von Neumann
entropy is at a maximum, corresponding to maximum entanglement.

--https://en.wikipedia.org/wiki/Quantum_entanglement​

Aha, alles klar. In this context you are talking of thermodynamics, from which it follows you are considering a thermodynamic ensemble, rather than individual QM entities. In such a context, one can of course envisage an ensemble in which some of the constituent QM entities are entangled with each other while some are not, and the proportion of each may differ from case to case such that one ensemble displays only a "weak" degree of entanglement while another has a "maximal" degree of it.

 

[arfa brane]

But again this seems to me distinct from what I would call proper entanglement, as I can't quite see how there is anything in this case where determination of the state of one entity automatically allows the state of the other to be known. It is mysterious, just as the double slit experiment is mysterious, but just as the double slit experiment is not entanglement, I don't - so far - see why this would be.

There isn't any "proper" entanglement.

What do you think of that part of a quote I posted that says the photons in a beam of sunlight coming through a window are "weakly entangled"? Entanglement is perhaps a lot more general than you think (maybe than most people think).

And the literature on entanglement entropy is quite large and growing; you could try google, but the results will be many and varied . . .

It seems the entropy measures connect entanglement to information theory, in a kind of really obvious way.

In this context you are talking of thermodynamics, from which it follows you are considering a thermodynamic ensemble, rather than individual QM entities.

The lifted graph is for a bipartite quantum system, not a thermodynamic ensemble. As it shows, the entanglement (von Neumann) entropy has a maximum and a minimum value.

 

[exchemist]

There isn't any "proper" entanglement.

What do you think of that part of a quote I posted that says the photons in a beam of sunlight coming through a window are "weakly entangled"? Entanglement is perhaps a lot more general than you think (maybe than most people think).

And the literature on entanglement entropy is quite large and growing; you could try google, but the results will be many and varied . . .

It seems the entropy measures connect entanglement to information theory, in a kind of really obvious way.The lifted graph is for a bipartite quantum system, not a thermodynamic ensemble. As it shows, the entanglement (von Neumann) entropy has a maximum and a minimum value.

I don't understand why the beam of sunlight is said to be weakly entangled, as the quote does not explain this. What would give rise to such entanglement? Though if some of the photons are entangled and some are not, then I can see the ensemble might be said to be weakly entangled, in some sense.

As for the von Neumann entropy thing, you are right. I have made an error. Von Neumann entropy can evidently apply to discrete pairs of QM entities. But I still don't see what it means to say an individual pair of QM entities is "weakly" entangled. Can you explain this?

 

[arfa brane]

So there is nothing special about us as observers being able to restrict interactions between quantum states, and get useful kinds of results from the eventual statistics.

There is no reason to presume, therefore, that entanglement post-interaction is not quite general, and so will need to be part of a theory of quantum gravity. After all gravity is a pretty general thing--if gravitational entropy is connected to entanglement entropy, there we have it.

The Holographic Principle perhaps illustrates this approach best, at least for now.

Here the theory says the third spatial dimension emerges from entanglement 'relations' between particles glued to a boundary, for example. They don't have much experimental backing yet either, but, there should be some 'information' in the CMB (how come that has anything to do with entanglement and quantum field theories?).

 

[exchemist]

So there is nothing special about us as observers being able to restrict interactions between quantum states, and get useful kinds of results from the eventual statistics.

There is no reason to presume, therefore, that entanglement post-interaction is not quite general, and so will need to be part of a theory of quantum gravity. After all gravity is a pretty general thing--if gravitational entropy is connected to entanglement entropy, there we have it.

The Holographic Principle perhaps illustrates this approach best, at least for now.

Here the theory says the third spatial dimension emerges from entanglement 'relations' between particles glued to a boundary, for example. They don't have much experimental backing yet either, but, there should be some 'information' in the CMB (how come that has anything to do with entanglement and quantum field theories?).

I don't deny there is much that is thought-provoking in what you say, but I really would prefer it if you could answer some of the questions I have posed, which remain unaddressed at the moment. What about the beam of sunlight? What about absorption interactions, going from 2 QM entities to one? What about simple molecular collisions?

As far as entanglement and von Neumann entropy is concerned, if entanglement were as widespread as you suggest, would you not expect that entropy effects from varying degrees of it should be visible in the measured entropy of macroscopic matter?

 

[arfa brane]

On the use of the term "weak" re entanglement and measurement.

If you perform repeated weak measurements of an entangled state it keeps the state coherent--this is the quantum Zeno effect.
Suppose you have an isotope atom with a probability of decaying, weak measurements can keep the atom 'entangled' with its non-decayed state.

Weak entanglement can be envisioned by the use of an ancillary 'particle' which entangles two others without itself becoming entangled with either (or always being weakly entangled). Anyways, here is a paper: http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/39/099/39099049.pdf
in which all is discussed starting about p11.