# What additional events must happen to produce entanglement

1. Feb 22, 2016

### sciencejournalist00

We all know how classical interference of waves can be produced by the Michaelson interferometer using the beam splitter and the detectors. No other elements needed to produce classical interference of waves.

Setups like this one which create quantum entanglement http://arxiv.org/abs/1212.6136 use beam splitter and detectors, but also use polarizers, wave plates, phase shifters and other elements together to entangle previously separable states.

Well, I am not an expert in quantum physics, only in classical physics, so I do not understand the difference between quantum entanglement and classical interference and what is the role that other elements play in the entanglement setup.

Could you explain to me what role do these other elements have? Why isn't the basic Michaelson interferometer used instead? What is the role of each element?

2. Feb 23, 2016

### stevendaryl

Staff Emeritus
Entanglement and interference are completely different concepts, and have nothing directly to do with each other.

Interference is just a consequence of superpositions. Classically, if you have two slits that allow light to pass into a box and onto a screen, the intensity of light at any point is the result of interference between light coming through the two slits. That interference can be constructive, leading to a brighter spot than you would have with just one slit. Or it can be destructive, leading to a dimmer spot than you would have with just one slit. Interference is a general property of waves, and classically phenomena such as light and sound show interference. Quantum mechanically, particles such as electrons also show interference.

Entanglement is about the inability to factor the states of two different subsystems or particles. Classically, if I have two objects, I can factor the states of the two objects, in the sense that I can tell you what state the first object is in, and tell you what state the second object is in, and together those two pieces of information tell you everything there is to know about the two-object composite system. Their states are not entangled. In general, in quantum mechanics, the state of a composite system cannot be factored way. You can't describe the whole system by giving the states of each component separately.

I think classical probabilities give a pretty good intuitive picture of entanglement. Suppose I have a pair of shoes, one left shoe and one right shoe, and I split them into two different boxes, and send one box to Alice, and another box to Bob. Then before Alice opens her box to see what's inside, she might describe her box probabilistically: It's 50% likely to contain a left shoe, and 50% likely to contain a right shoe. Bob would describe his box the same way. But the total system, consisting of the two boxes, are not completely described by those two descriptions. There is an additional constraint: If Alice's box contains a left shoe, then Bob's box contains a right shoe, and if Alice's box contains a right shoe, then Bob's box contains a left shoe. This constraint is a constraint on the state of the total system, and isn't deducible from the states of Alice's box and Bob's box separately. (If there were no such constraint, then there would be a 25% that both boxes would contain a left shoe.) So the probabilistic descriptions of Alice's and Bob's boxes are entangled : there is information about the total system above and beyond the descriptions of the components.

Now, here's the difference between classical probabilities, which have a notion of "entanglement", and quantum entanglement: In the case of classical probabilities, apparent entanglement can always be explained as being due to lack of information about the true state of the system. If Alice knew exactly the state of her box, she would describe it as "a box containing a left shoe" (or whichever one it was), and if Bob knew exactly the state of his box, he would describe it in the opposite way. So if Alice and Bob had complete information, then the states of their boxes would not be entangled---the state of the composite, two-box system would be completely described by the states of each box separately. So the appearance of entanglement is due to lack of information. In the quantum case, there is a notion of entanglement that is apparently not due to lack of information. The state of a composite system may simply not be describable by separately giving the states of all the components.

3. Feb 23, 2016

### sciencejournalist00

But the experiment in the link I have given uses interference of fluorescence photons from two nitrogen-vacancy centers in two diamonds at a beam splitter to generate entanglement. Lilian Childress is not a basic physics teacher, she has many recognized papers published in online journals.

You are going back to the primitive definition of entanglement, ignoring all the research that scientists have published.

4. Feb 23, 2016

### stevendaryl

Staff Emeritus
You asked what was the difference between interference and entanglement, and I told you. They are completely different concepts.

5. Feb 23, 2016

### stevendaryl

Staff Emeritus
Suppose someone asked you "What is the difference between an aardvark and an architect?" I assume that you would give the basic definitions of the two terms: one is an animal that eats ants, and the other is a person who designs buildings. If the person then followed up by saying "I don't want the elementary-school explanation of the difference, I want a more modern, cutting-edge explanation?", how would you answer, then?

6. Feb 23, 2016

### drvrm

we know superposition in classical waves or quantum mechanical systems which leads to interference effects..
the prime question is how entanglement gives a new way of non-local connectivity
Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the state of each particle cannot be described independently — instead, a quantum state may be given for the system as a whole.

measurements of physical observables e.g. position q, momema p , spin s,etc., performed on entangled particles are found to be appropriately correlated.
For example, if two particles is generated in such a way that their total spin is known to be zero,
and one particle is found to have spin up then the spin of the other will be down

this produces paradoxes: any quantum measurement is by collapsing a number of superposed states);
therefore for entangled particles, such action must be on the entangled system as a whole.
It may appear that one particle of an entangled pair "knows" what measurement has been performed on the other, and with what outcome, even if there is no way for such information to be communicated between the particles. and they may be far from each other

Einstein and others considered such behavior to be impossible, as it violated the local realist view of causality. Later, however, the counter intuitive predictions of quantum mechanics were verified experimentally.Experiments have been performed involving measuring the polarization or spin of entangled particles in different directions, which — by producing violations of Bells inequality — these experiments contested the view of local realism.
According to the formalism of quantum theory, the effect of measurement happens instantly.

see details <wiki-quantum entanglement)

7. Feb 23, 2016

### sciencejournalist00

There is a difference between self-interference of photons that you call interference in your post, and two-photon interference that you ignore. The first creates superposition between the many trajectories of the same photon, while the second creates entanglement between two photons IF some additional conditions are fulfilled. What are these conditions?

Two - photon interference (the four possibilities of two-photon reflection and transmission are added at the amplitude level):

Difference between self-interference and two-photon interference

8. Feb 23, 2016

### sciencejournalist00

Single-particle quantum interference

Interference fringes can be observed in a two-path interferometer if there is no way of knowing, not even in principle, which path the particle takes. In a MachZehnder interferometer a quantum particle strikes a beam splitter and has a 50/50 chance of being transmitted or reflected. Mirrors reflect both paths so that they meet at a second 50/50 beam splitter, and the numbers of particles transmitted/reflected by this beam splitter are counted. If no information about the path is available, the particle is in a superposition of the upper and lower paths. To observe interference one customarily varies the length of one of the paths (e.g. with a variable wave plate) and counts single clicks at the detectors as a function of this phase.

Two-particle quantum interference

When two particles are incident symmetrically on a 50/50 beam splitter it is possible for both to emerge in either the same beam (left) or in different beams (right). In general, bosons (e.g. photons) emerge in the same beam, while fermions (e.g. electrons) emerge in different beams. The situation is more complex for entangled states, however, and two photons in the Bell state |Y> emerge in different beams. Therefore, if detectors placed in the two outward directions register photons at the same time, the experimenter knows that they were in a |Y> state. Moreover, because we do not know the paths followed by the photons, they remained entangled.

Decay into daughter particles

When an ultraviolet laser beam strikes a crystal of beta barium borate, a material with nonlinear optical properties, there is a small probability that one of the photons will spontaneously decay into a pair of photons with longer wavelengths (to conserve energy). The photons are emitted in two cones and propagate in directions symmetric to the direction of the original UV photon (to conserve momentum). In so-called type II parametric down-conversion, one of the photons is polarized horizontally and the other is polarized vertically. It is possible to arrange the experiment so that the cones overlap (see photograph). In this geometry the photons carry no individual polarizations all we know is that the polarizations are different. This is an entangled state. (P G Kwiat et al. 1995 Phys. Rev. Lett. 75 4337)

9. Feb 23, 2016

### sciencejournalist00

Again, I ask you, what are the conditions for two-photon interference to generate entanglement?

10. Feb 24, 2016

### bhobba

http://www2.mpq.mpg.de/Theorygroup/CIRAC/wiki/images/7/78/Ahsan.pdf

Have you the background to understand it? Are you any wiser?

I have read a lot of books on QM and it will take me quite a while to understand it. When photons enter crystals, prisms etc some very complex things happen. They create quasi particles and those quasi particles are converted back to photons when they exit. It's obviously something going on inside that when they exit some are entangled.

I have zero idea why you want to understand the technical details without a good knowledge of QM - it''s obvious it cant be done. What do you want - someone with that technical knowledge to chug though it and sort it out then translate it into lay terms? I have news for you - well before that level the jig is up on explaining things in lay terms. Even explaining a fundamental concept like what entanglement is in lay terms is impossible. Once you know the technicalities is quite trivial, but without those forget it.

Thanks
Bill

Last edited: Feb 24, 2016
11. Feb 24, 2016

### sciencejournalist00

I am not intelligent enough to understand the difference between shared coherent states and shared entangled states, or how that setup operates. If I were, I would not be asking questions.

Maybe a shared coherent state would be |V>|V> or |H>|H>, while a shared entangled state would be 1/sqrt(2) |H>|V> + |V>|H>?

The separation between entanglement and interference dates back to the time when scientists used only atomic cascade decay or radioactive decay to generate entangled pairs, and only classical waves to produce interference patterns.

From classical physics, I know the beam splitter produces interference patterns within the Michaelson interferometer when two coherent waves are incident on it.

Modern interferometers can also generate entanglement as long as they have additional elements added. What is the role of these additional elements? and what interactions they create between photons and how they work together with the beam splitter is beyond my understanding.

12. Feb 24, 2016

### bhobba

Precisely what don't you get about explain that at the lay level cant be done?

As I said I think I know QM pretty well and it will take me quite a slog to sort it out. The chances of explaining it in lay terms will be zero. However it seems likely its got something to do with the quasi particles inside those elements you talk about. For example that's how a polariser works - and even that is quite difficult and advanced to understand.

See:
https://www.physicsforums.com/insights/do-photons-move-slower-in-a-solid-medium/

Thanks
Bill

Last edited: Feb 24, 2016
13. Feb 24, 2016

### stevendaryl

Staff Emeritus
I'm ignoring it because you asked what the difference between interference and entanglement. The difference between self-interference and two-photon interference is not relevant to the question of what is the difference between interference and entanglement. There are several types of aardvarks, but that isn't really relevant to the question: What's the difference between an aardvark and an architect?

14. Feb 24, 2016

### stevendaryl

Staff Emeritus
An entangled state of two particles is any state that is NOT a simple product state. $|V\rangle |V\rangle$ is a product state: the first particle is in state $|V\rangle$ and the second particle is also in state $|V\rangle$. The state $1/\sqrt(2)( |H\rangle |V\rangle + |V\rangle|H\rangle)$ is not a product state, so it's an entangled state.

It is possible to use a beam-splitter to make two photons become entangled: https://physics.aps.org/articles/v7/25

15. Feb 24, 2016

### Mentz114

My reading of that note is that each of those (bold) photons must belong to an entangled pair. This entanglement is transferred to one from each pair. I think the OP needs to be aware of that.

16. Feb 24, 2016

### DrChinese

Good point, and we have explained that several times. These are complex experiments with many details, and it is easy to pick out phrases - without the critical associated detail - and end up with the wrong impression.

He has asked: What is the role of the additional elements in the setups that create entanglement? The answer: the ENTIRE context of a setup must be considered in a quantum experiment (really any experiment). This context is created by really intelligent scientists who have been studying this for years, and building on ideas presented in hundreds of published articles on the subject. There are literally hundreds of ways to create entanglement using the various building blocks (elements). The OP has previously indicated no desire to learn about these.

There is no one single formula which is used in all cases to create entanglement. For example, parametric down conversion creates entanglement in a fundamentally different manner than atomic cascades. And generally, you cannot entangle photons using a beam splitter alone.

17. Feb 24, 2016

### naima

Stevendaryl wrote:
Entanglement and interference are completely different concepts, and have nothing directly to do with each other.

DrChinese wrote:
There is no interference UNLESS you first make the light coherent by diffracting it through a pinhole or similar. Entangled photons are not coherent.

Are you talking about the same notion of coherence?

What do you think of this?

It reminds me DrChinese remark about pinholes.

Last edited: Feb 24, 2016
18. Feb 24, 2016

### sciencejournalist00

Entangled photons on their own are not coherent because they are described by mixed states.
However, the entangled system of photons is coherent because it is found in a pure state.

In classical scattering of target body by environmental photons, the motion of the target body will not be changed by the scattered photons on the average. In quantum scattering, the interaction between the scattered photons and the superposed target body will cause them to be entangled, thereby delocalizing the phase coherence from the target body to the whole system, rendering the interference pattern unobservable.

19. Feb 25, 2016

### sciencejournalist00

While the beam splitter needs additional elements to create entanglement between photons, it does not need these elements to create entanglement between atoms.

A single photon in superposition, when absorbed by two objects, creates entanglement between them.
There is no need for elements to prepare the photon for superposition, as superposition is an intrinsic property of the photon

A heralded single photon (the 'pea') first passes through a beamsplitter. The outputs of the beamsplitter are directed to the two crystals (the 'shells'), where the photon is absorbed to produce a single excitation. The lack of information regarding the path of the photon creates an entangled state between the two crystals.

20. Feb 25, 2016

### sciencejournalist00

Tell me please what you understand from this below quote of an entanglement protocol:

"Both centres NV A and NV B are initially prepared in a superposition 1/ √ 2(|↑>+ |↓>). Next, each NV centre is excited by a short laser pulse that is resonant with the |↑> to |e> transition, where |e> is an optically excited state with the same spin projection as |↑>.

Spontaneous emission locally entangles the qubit and photon number, leaving each setup in the state 1/ √ 2(|↑ 1> + |↓ 0>), where 1 (0) denotes the presence (absence) of an emitted photon;

The two photon modes, A and B, are directed to the input ports of a beamsplitter, so that fluorescence observed in an output port could have originated from either NV centre. If the photons emitted by the two NV centres are indistinguishable, detection of precisely one photon on an output port would correspond to measuring the photon state |1A0B>±e^ −iϕ |0A1B> (where ϕ is a phase that depends on the optical path length). Such a detection event would thereby project the qubits onto the maximally entangled state |ψ> = 1/ √ 2(|↑A↓B> ± e −iϕ |↓A↑B>)."