Quantum entanglement by the means of beam splitters

[sciencejournalist00]

I saw many of you saying in their posts that non-linear crystals like barium borate are the only means of producing entangled photons. And because they are expensive, only some of you can afford them.

But I browsed the international science magazines and found this:

https://physics.aps.org/articles/v7/25

"Photons are often entangled at their creation. For example, pairs of identical photons can be generated by “down-converting” single pump photons in a nonlinear crystal. Unfortunately, this process is inefficient because the down-conversion has a low probability.

One alternative is to entangle photons coming from different sources. This can be done by sending two photons into a beam splitter and taking advantage of the quantum phenomenon of two-photon interference: If an observer behind the beam splitter cannot tell which path each individual photon took, their probabilistic outcomes can add up or cancel out, leaving those photons that exit the beam splitter through different ports in an entangled state. This effect has been the workhorse of the quantum photonics community for decades."

http://www.livescience.com/19975-spooky-quantum-entanglement.html

"The way you entangle them is to send them onto a half-silvered mirror," Zeilinger told LiveScience. "It reflects half of the photons, and transmits half. If you send two photons, one to the right and one to the left, then each of the two photons have forgotten where they come from. They lose their identities and become entangled."

As you can see, entanglement can be done by a beam splitter for two photons, because this beam splitter creates an identical superposition of trajectories for both photons. We do not know if the photon coming from the left is transmitted or if the photon coming from the right is reflected, and their trajectories coincide.

 

[sciencejournalist00]

I am asking you if beam splitters entangle photons because I am planning to write an article about a quantum processor based on a multi-port beam splitter which would function as a data bus. This quantum processor can only work if beam splitters do entangle photons. If they don't, I have to use another element that produces entanglement

 

[DrChinese]

http://www.livescience.com/19975-spooky-quantum-entanglement.html

"The way you entangle them is to send them onto a half-silvered mirror," Zeilinger told LiveScience. "It reflects half of the photons, and transmits half. If you send two photons, one to the right and one to the left, then each of the two photons have forgotten where they come from. They lose their identities and become entangled."

As you can see, entanglement can be done by a beam splitter for two photons, because this beam splitter creates an identical superposition of trajectories for both photons. We do not know if the photon coming from the left is transmitted or if the photon coming from the right is reflected, and their trajectories coincide.

Welcome to PhysicsForums, sciencejournalist00!

You only quoted from part of the paper. The process Zeilinger describes is quite different than you imagine. I would recommend you read the entire paper, or here is one he wrote which is equivalent:

http://arxiv.org/abs/quant-ph/0201134

The process actually entangles 2 entirely different photons elsewhere (nowhere near the beam splitter). Further, the entanglement can be in 2 different states: + or -. One yield symmetric polarization, the other is anti-symmetric. These occur randomly, so there is not a lot you can do with the resulting entangled pair for computing purposes.

 

[PietKuip]

I saw many of you saying in their posts that non-linear crystals like barium borate are the only means of producing entangled photons. And because they are expensive, only some of you can afford them.

There is also this way:
http://blogs.scientificamerican.com...-quantum-entanglement-experiment-part-1-of-2/
http://www.diyphysics.com/2013/02/1...eapest-demonstration-of-quantum-entanglement/

It uses the gamma photons from positron annihilation.

 

[sciencejournalist00]

You seem to forget something. Zeilinger describes a quantum teleportation experiment, with two sources of entanglement. First an entangled pair from a nonlinear crystal is created and another independent photon will be entangled with a member of the pair with the help of a beam splitter. One member is entangled with the independent photon at Alice's location in the Bell measurement process and another member of the pair is sent at Bob's location.

The entanglement of the independent photon with a member of the pair, makes both members of the pair at both locations adopt its polarization state, and this is how the state of the independent photon is teleported to Bob's location.

Also
http://www.nature.com/nphoton/journal/v6/n4/fig_tab/nphoton.2012.68_F2.html

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.

http://www.kurzweilai.net/diamond-shows-promise-for-a-quantum-internet

To entangle qubits in separate pieces of diamond, the team uses lasers to entangle each qubit with a photon at temperatures of 10 kelvin. The photons meet midway through a fibre-optic cable, where they are themselves entangled. The ZPL photons from the two NV centres are overlapped on a fibre-coupled beamsplitter.

http://www.2physics.com/2011/12/entang-bling.html

A single photon (filled circle) cannot divide into two when it hits a beam splitter. It must either pass through, or be reflected. According to quantum mechanics, both of these possibilities occur, producing an entangled state, in which a single photon is shared between the two beams after the beam splitter. Running this process in reverse (i.e. from right to left) provides a way to detect entanglement, since only an entangled state will always produce a single photon in the same place on the left.

 

[sciencejournalist00]

http://www.nature.com/nphys/journal/v3/n10/full/nphys700.html
Entangling independent photons by time measurement
Remarkably, entanglement can be 'swapped': if we prepare two independent entangled pairs A1–A2 and B1–B2, a joint measurement on A1 and B1 (called a 'Bell-state measurement', BSM) has the effect of projecting A2 and B2 onto an entangled state, although these two particles have never interacted nor share any common past

http://iontrap.umd.edu/research/ion-photon-quantum-networks/
Quantum computer based on entanglement of trapped ions
The single photons from ions in separate traps are collected and directed to a 50:50 beamsplitter. Due to the quantum interference of the photons (Nature Physics 3, 538 (2007)), detection of certain Bell states of light upon exiting the beam splitter projects the atoms into an entangled state. For example, only an antisymmetric photonic state will result in a simultaneous detection at both output ports of the beamsplitter. It is this “double-click” of the detectors that heralds the entanglement of the two ions.

 

[sciencejournalist00]

Is there any more doubt? Nature is peer reviewed... not out of a kid's imagination. It clearly says in Nature that photons do not need to be created together to be entangled, a Bell measurement can entangle photons from different sources.

Also, pairs of matter particles that interact by collision also become entangled, because momenta depend on each other after a collision. This one I got from Albert Einstein's article in 1935:“Suppose two particles are set in motion towards each other with the same, very large, momentum, and that they interact with each other for a very short time when they pass at known positions. Consider now an observer who gets hold of one of the particles, far away from the region of interaction, and measures its momentum; then, from the conditions of the experiment, he will obviously be able to deduce the momentum of the other particle. If, however, he chooses to measure the position of the first particle, he will be able to tell where the other particle is. This is a perfectly correct and straightforward deduction from the principles of quantum mechanics; but is it not very paradoxical? How can the final state of the second particle be influenced by a measurement performed on the first, after all physical interaction has ceased between them? "(Einstein, A.; Podolsky, B.; Rosen, N. (1935). "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?")

 

[sciencejournalist00]

Welcome to PhysicsForums, sciencejournalist00!

You only quoted from part of the paper. The process Zeilinger describes is quite different than you imagine. I would recommend you read the entire paper, or here is one he wrote which is equivalent:

http://arxiv.org/abs/quant-ph/0201134

The process actually entangles 2 entirely different photons elsewhere (nowhere near the beam splitter). Further, the entanglement can be in 2 different states: + or -. One yield symmetric polarization, the other is anti-symmetric. These occur randomly, so there is not a lot you can do with the resulting entangled pair for computing purposes.

DrChinese, you said that paper says the beam splitter does not play role in entanglement.

What it says is there are initially two pairs of entangled photons 0-1 and 2-3 independent from one another which were created by a nonlinear crystal, and the beam splitter entangles the two pairs:

Initially, the system is composed of two independent entangled states psi01 and psi23.Alice subjects photons 1 and 2 to a measurement in a Bell-state analyzer (BSA), and if she finds them in the state psi12, then photons 0 and 3 measured by Bob, will be in the entangled state psi03.

We stress that photons 0 and 3 will be perfectly entangled for any result of the BSA, and therefore it is not necessary to apply a unitary operation to the teleported photon 3 as in the standard teleportation protocol.

 

[sciencejournalist00]

I am posting these references because I need advice to interpret them right. My conclusion would be that a beam splitter is the only thing I would need to create entanglement, but I am not sure! I need interpretations from more people in order to be sure.

 

[DrChinese]

Is there any more doubt? Nature is peer reviewed... not out of a kid's imagination. It clearly says in Nature that photons do not need to be created together to be entangled, a Bell measurement can entangle photons from different sources.

DrChinese, you said that paper says the beam splitter does not play role in entanglement.

No doubt, these experiments are all good. It's your conclusion(s) that are in question. I never said the beam splitter does not play a role in the process for example, clearly it is a critical component. You also said:

"My conclusion would be that a beam splitter is the only thing I would need to create entanglement."

But you cannot entangle random photons in a beam splitter. The actual setup is very sophisticated, and there are many details that are being glossed over with a statement like the above. For example: You might notice that photons emerging from a beam splitter (Bell State Analyzer) are polarized. Therefore they themselves are not polarization entangled. What is now entangled are the 0 and 3 photons. They are not random photons, but rather created (by processes which vary from paper to paper) using very special setups that create entangled states. So the general rule is that the BSA is used for entanglement swapping between already entangled pairs, not for creating original entangled pairs. You even say the same thing as this:

"What it says is there are initially two pairs of entangled photons 0-1 and 2-3 independent from one another which were created by a nonlinear crystal, and the beam splitter entangles the two pairs:"

Anybody here is going to tell you the same thing using different words. Also, I believe you will find that although the 0-1 and 2-3 pairs are created independently (in one usage of the word), in all variations of the setup there is phase locking between the source lasers. In other words, independent pulses are timed to be synchronized so that the phases are matched. This is critical to the experiment, and certainly no piece of cake to perform properly. This is done before the photons ever arrive at the BSA.

So you seem to understand the experiment well enough, and believe me these are state of the art and not easy to follow. But you might want to try cleaning up your conclusions a bit. In your post #2 you say: "This quantum processor can only work if beam splitters do entangle photons." You were apparently trying to avoid the use of BBO crystal for entanglement, but the reality is that the beam splitter is just a component of a much more complex system. That entire system is not going to fit very well on a chip, and certainly is not going to be simpler than a BBO crystal.

For obtaining entangled pairs on demand: substantial research is being performed to the end of being able to create an entangled pair via some mechanism that could be reproduced at the chip level. This is a very difficult and complex problem to put it mildly. I can point you in some directions if you want to get a feel for where people are going with that.

 

[sciencejournalist00]

No doubt, these experiments are all good. It's your conclusion(s) that are in question. I never said the beam splitter does not play a role in the process for example, clearly it is a critical component. You also said:

"My conclusion would be that a beam splitter is the only thing I would need to create entanglement."

But you cannot entangle random photons in a beam splitter. The actual setup is very sophisticated, and there are many details that are being glossed over with a statement like the above. For example: You might notice that photons emerging from a beam splitter (Bell State Analyzer) are polarized. Therefore they themselves are not polarization entangled. What is now entangled are the 0 and 3 photons. They are not random photons, but rather created (by processes which vary from paper to paper) using very special setups that create entangled states. So the general rule is that the BSA is used for entanglement swapping between already entangled pairs, not for creating original entangled pairs. You even say the same thing as this:

"What it says is there are initially two pairs of entangled photons 0-1 and 2-3 independent from one another which were created by a nonlinear crystal, and the beam splitter entangles the two pairs:"

Anybody here is going to tell you the same thing using different words. Also, I believe you will find that although the 0-1 and 2-3 pairs are created independently (in one usage of the word), in all variations of the setup there is phase locking between the source lasers. In other words, independent pulses are timed to be synchronized so that the phases are matched. This is critical to the experiment, and certainly no piece of cake to perform properly. This is done before the photons ever arrive at the BSA.

So you seem to understand the experiment well enough, and believe me these are state of the art and not easy to follow. But you might want to try cleaning up your conclusions a bit. In your post #2 you say: "This quantum processor can only work if beam splitters do entangle photons." You were apparently trying to avoid the use of BBO crystal for entanglement, but the reality is that the beam splitter is just a component of a much more complex system. That entire system is not going to fit very well on a chip, and certainly is not going to be simpler than a BBO crystal.

For obtaining entangled pairs on demand: substantial research is being performed to the end of being able to create an entangled pair via some mechanism that could be reproduced at the chip level. This is a very difficult and complex problem to put it mildly. I can point you in some directions if you want to get a feel for where people are going with that.

What about this experiment with trapped ions in which the only things used to entangle the ions are the beam splitter and detectors?

http://phys.org/news/2012-07-quantum-entanglement-notification.html
An experimental set-up, consisting of a beam splitter and two photo detectors, registers the photons emitted by the rubidium atoms (red beam) and generates a signal whenever the two atoms are in an entangled stated (illustrated by violet beams). Graphic: Wenjamin Rosenfeld

http://arxiv.org/pdf/0801.1595.pdf

What about this experiment which uses single photons incident on a beamsplitter?

 

[zonde]

What about this experiment with trapped ions in which the only things used to entangle the ions are the beam splitter and detectors?

http://phys.org/news/2012-07-quantum-entanglement-notification.html
An experimental set-up, consisting of a beam splitter and two photo detectors, registers the photons emitted by the rubidium atoms (red beam) and generates a signal whenever the two atoms are in an entangled stated (illustrated by violet beams). Graphic: Wenjamin Rosenfeld

This article does not describe details of experiment. It seems you can get original paper just by registering.
This is similar experiment:
http://arxiv.org/abs/1508.05949
Here you can read that entanglement scheme is a bit more complex than simultaneously registering two photons at two outputs of beamsplitter. If you look at Fig.3b it shows that identical photons can not be registered simultaneously at different output ports of beamsplitter (because of HOM effect) when photons are identical. Instead they are registered at a certain delay. Further details are beyond my knowledge.

http://arxiv.org/pdf/0801.1595.pdf

What about this experiment which uses single photons incident on a beamsplitter?

This paper does not describe experiment, only proposal. And two photons should be in the same input of beamsplitter.

 

[sciencejournalist00]

The basic concept is to create entanglement between two atoms, which are separated in space, with the help of photons, and to transfer this state onto succeeding atoms (stationary quantum systems respectively). Hence, two rubidium atoms, each captured inside an optical dipole trap, are stimulated by light pulses from a control laser to emit a photon. In this process the quantum state of the atom is entangled with the polarization state of the photon. Travelling through separate glass fibres the two photons reach a beam splitter where they are brought to interference. The simultaneous detection of two photons at different output ports of the beam splitter gives notice of successful entanglement. In absence of a signal the whole procedure is repeated. “We have to try for about a million times”, Professor Weinfurter explains the experimental difficulties which are mainly due to the loss of photons during their coupling to the glass fibre. “The confirmation of entanglement makes it easier to connect several such systems in series, like a chain, thereby extending the entanglement over the whole chain. Without such a signal we would have to use much more complex methods for the generation of entanglement.”

Read more at: http://phys.org/news/2012-07-quantum-entanglement-notification.html#jCp

 

[sciencejournalist00]

This article does not describe details of experiment. It seems you can get original paper just by registering.
This is similar experiment:
http://arxiv.org/abs/1508.05949
Here you can read that entanglement scheme is a bit more complex than simultaneously registering two photons at two outputs of beamsplitter. If you look at Fig.3b it shows that identical photons can not be registered simultaneously at different output ports of beamsplitter (because of HOM effect) when photons are identical. Instead they are registered at a certain delay. Further details are beyond my knowledge.This paper does not describe experiment, only proposal. And two photons should be in the same input of beamsplitter.

You wanted a link to the full paper?

http://xqp.physik.uni-muenchen.de/publications/files/articles_2012/science_337_72.pdf

 

[zonde]

You wanted a link to the full paper?

http://xqp.physik.uni-muenchen.de/publications/files/articles_2012/science_337_72.pdf

In Fig.1a you can see that they use PBSes and in the text you can find that they single out entangled states where polarizations of photons are different (H and V).

If you use just beamsplitter you get HOM interference where identical photons appear on the same output of beamsplitter. That's it.

 

[sciencejournalist00]

What zonde said about that paper, not all elements in the circuit entangle light. We generate entanglement between the two distant spins by entanglement swapping in the Barrett-Kok
scheme using a third location C (roughly midway
between A and B, see Fig. 1e). First we entangle each
spin with the emission time of a single photon (time-bin encoding). The two photons are then sent to location C, where they are overlapped on a beam-splitter
and subsequently detected. If the photons are indistinguishable in all degrees of freedom, the observation of one early and one late photon in dierent output ports
projects the spins at A and B into the maximally entangled state

 

[DrChinese]

1.What about this experiment with trapped ions in which the only things used to entangle the ions are the beam splitter and detectors?

http://phys.org/news/2012-07-quantum-entanglement-notification.html
An experimental set-up, consisting of a beam splitter and two photo detectors, registers the photons emitted by the rubidium atoms (red beam) and generates a signal whenever the two atoms are in an entangled stated (illustrated by violet beams). Graphic: Wenjamin Rosenfeld

http://arxiv.org/pdf/0801.1595.pdf

2. What about this experiment which uses single photons incident on a beamsplitter?

1. Yes, I'm familiar with this. Again, you are ignoring the rest of the apparatus and focusing on the beam splitter, which is a component. You may as well say that it only takes a laser to create entanglement.

2. This is not an experiment, it is a theoretical study. And again, note that there is a complex apparatus in the proposal. And the photons are not polarization entangled, so ordinary bit type operations are not possible.

 

[sciencejournalist00]

In Fig.1a you can see that they use PBSes and in the text you can find that they single out entangled states where polarizations of photons are different (H and V).

If you use just beamsplitter you get HOM interference where identical photons appear on the same output of beamsplitter. That's it.

No, PBS are the elements that work with detectors to measure polarization in what is called homodyne detection. They do not entangle anything.
And HOM interference with two identical photons on the same output is still an entangled state from a class called NOON states.

https://en.wikipedia.org/wiki/Hong–Ou–Mandel_effect#Applications_and_experiments
The Hong–Ou–Mandel effect also underlies the basic entangling mechanism in linear optical quantum computing, and the two-photon quantum state

that leads to the HOM dip is the simplest non-trivial state in a class called NOON states.

 

[sciencejournalist00]

1. Yes, I'm familiar with this. Again, you are ignoring the rest of the apparatus and focusing on the beam splitter, which is a component. You may as well say that it only takes a laser to create entanglement.

2. This is not an experiment, it is a theoretical study. And again, note that there is a complex apparatus in the proposal. And the photons are not polarization entangled, so ordinary bit type operations are not possible.

But it shows nonlinear crystals are not necessary, right? That linear optics alone can entangle light.

 

[DrChinese]

The basic concept is to create entanglement between two atoms, which are separated in space, with the help of photons, and to transfer this state onto succeeding atoms (stationary quantum systems respectively). Hence, two rubidium atoms, each captured inside an optical dipole trap, are stimulated by light pulses from a control laser to emit a photon. In this process the quantum state of the atom is entangled with the polarization state of the photon. Travelling through separate glass fibres the two photons reach a beam splitter where they are brought to interference. The simultaneous detection of two photons at different output ports of the beam splitter gives notice of successful entanglement. In absence of a signal the whole procedure is repeated. “We have to try for about a million times”, Professor Weinfurter explains the experimental difficulties which are mainly due to the loss of photons during their coupling to the glass fibre. “The confirmation of entanglement makes it easier to connect several such systems in series, like a chain, thereby extending the entanglement over the whole chain. Without such a signal we would have to use much more complex methods for the generation of entanglement.”

Read more at: http://phys.org/news/2012-07-quantum-entanglement-notification.html#jCp

I can see that you are reading the right words. Do you know what they are actually saying and how it relates to your original post? As I keep saying, this is a very complex and difficult setup and the beam splitter is just one component. If you still have some specific question, what is it?

 

[DrChinese]

But it shows nonlinear crystals are not necessary, right? That linear optics alone can entangle light.

There are dozens if not hundreds of ways to entangle things that do not involve nonlinear crystals. And no, simple linear optics alone are not enough to produce entanglement. Please re-read the experiments you are quoting from and you will see that there are numerous other critical elements to the process besides a PBS.

 

[sciencejournalist00]

I can see that you are reading the right words. Do you know what they are actually saying and how it relates to your original post? As I keep saying, this is a very complex and difficult setup and the beam splitter is just one component. If you still have some specific question, what is it?

http://www.2physics.com/2011/12/entang-bling.html

In this post it says the beam-splitter is the only needed element.

A single photon (filled circle) cannot divide into two when it hits a beam splitter. It must either pass through, or be reflected. According to quantum mechanics, both of these possibilities occur, producing an entangled state, in which a single photon is shared between the two beams after the beam splitter. Running this process in reverse (i.e. from right to left) provides a way to detect entanglement, since only an entangled state will always produce a single photon in the same place on the left.

and

After the beams are mixed on a beam splitter, it is impossible to tell which diamond the photon came from. This means there is one vibration shared between the two diamonds — they are entangled.

Do you see them saying that other elements are sources of entanglement?

https://en.wikipedia.org/wiki/Beam_splitter

In 2000 Knill, Laflamme and Milburn (KLM protocol) proved that it is possible to create universal quantum computer solely with beam splitters, phase shifters, photodetectors and single photon sources. The states that form a qubit in this protocol are the one photon states of two modes, i.e. the states |01> and |10> in the occupation number representation (Fock state) of two modes. Using these resources it's possible to implement any single qubit gate and 2-qubit probabilistic gates. The beam splitter is an essential component in this scheme since it's the only one that creates entanglement between the Fock states.

 

[DrChinese]

http://www.2physics.com/2011/12/entang-bling.html

In this post it says the beam-splitter is the only needed element.

A single photon (filled circle) cannot divide into two when it hits a beam splitter. It must either pass through, or be reflected. According to quantum mechanics, both of these possibilities occur, producing an entangled state, in which a single photon is shared between the two beams after the beam splitter. Running this process in reverse (i.e. from right to left) provides a way to detect entanglement, since only an entangled state will always produce a single photon in the same place on the left.

and

After the beams are mixed on a beam splitter, it is impossible to tell which diamond the photon came from. This means there is one vibration shared between the two diamonds — they are entangled.

Do you see them saying that other elements are sources of entanglement?

First, this is not a suitable reference to a peer reviewed paper. Second, again, you are reading words but failing to understand. Yes, things called "entangled states" are possible with single particles. But they don't work in quantum processing like entangled pairs do.

Please note: we are not having a debate about entanglement. You have asked some questions, and we are attempting to answer them.

 

[sciencejournalist00]

First, this is not a suitable reference to a peer reviewed paper. Second, again, you are reading words but failing to understand. Yes, things called "entangled states" are possible with single particles. But they don't work in quantum processing like entangled pairs do.

Please note: we are not having a debate about entanglement. You have asked some questions, and we are attempting to answer them.

Well, don't nonlinear crystals form entangled states only where the trajectories of vertical polarized photons and horizontal polarized photons coincide? At the intersection of the emission cones? Outside this intersection classical correlations are possible, but the polarization and the trajectories are distinguishable.

This is the same way beam splitters do. By making photons intersect their trajectories.

Plus, the authors of the Entang-bling on 2physics are http://www.physics.ox.ac.uk/al/people/walmsley.htm and http://www2.physics.ox.ac.uk/contacts/people/nunn from Clarendon Laboratory, Department of Physics, University of Oxford, UK.

It was copied from
http://iopscience.iop.org/article/10.1088/1742-6596/442/1/012004

 

[DrChinese]

Well, don't nonlinear crystals form entangled states only where the trajectories of vertical polarized photons and horizontal polarized photons coincide? At the intersection of the emission cones? Outside this intersection classical correlations are possible, but the polarization and the trajectories are distinguishable.

This is the same way beam splitters do. By making photons intersect their trajectories.

Plus, the authors of the Entang-bling on 2physics are http://www.physics.ox.ac.uk/al/people/walmsley.htm and http://www2.physics.ox.ac.uk/contacts/people/nunn from Clarendon Laboratory, Department of Physics, University of Oxford, UK.

It was copied from
http://iopscience.iop.org/article/10.1088/1742-6596/442/1/012004

The above is a suitable reference, and is different than what you posted earlier.

Again, you are mixing incompatible ideas. BBo crystals and PBSs are different. You cannot take 2 random photons and entangle them with a PBS. You must prepare them first. You cannot take a single photon and entangle it with a PBS either. Please note that the single photon entanglement you speak of is simply saying that a photon is in a superposition of polarization states. If it is polarized at a 45 degree angle (a superposition of H+V) then a PBS will reveal that. The PBS does not create any entanglement in this case - it pre-existed.

 

[sciencejournalist00]

The above is a suitable reference, and is different than what you posted earlier.

Again, you are mixing incompatible ideas. BBo crystals and PBSs are different. You cannot take 2 random photons and entangle them with a PBS. You must prepare them first. You cannot take a single photon and entangle it with a PBS either. Please note that the single photon entanglement you speak of is simply saying that a photon is in a superposition of polarization states. If it is polarized at a 45 degree angle (a superposition of H+V) then a PBS will reveal that. The PBS does not create any entanglement in this case - it pre-existed.

But they say in Nature that nonlinear crystals have entangled states only where the polarization is undefined because photons with different polarizations cross each others trajectory. In beam splitters, two photons incident from different ports also cross each other's trajectory. They may both be reflected or both transmitted, who knows? The direction each photon follows is unknown.

Outside the intersection cones, correlations in form of certain polarizations and certain trajectories are present due to conservation of momentum.

 

[DrChinese]

But they say in Nature that nonlinear crystals have entangled states only where the polarization is undefined because photons with different polarizations cross each others trajectory.

Yes, no one is disputing that for polarization entangled states. As I say, you are mixing and matching ideas that you are reading that have similar words. You must realize that each experiment is unique and presents its own elements. You can't take one from column A and one from column B like a menu. There are literally thousands of entanglement experiments, and they each explore a different idea around entanglement. So you must be specific to make good sense.

 

[sciencejournalist00]

Apparent Contradiction in EPR Correlations
http://link.springer.com/chapter/10.1007/978-94-011-5682-0_32

 

[sciencejournalist00]

Yes, no one is disputing that for polarization entangled states. As I say, you are mixing and matching ideas that you are reading that have similar words. You must realize that each experiment is unique and presents its own elements. You can't take one from column A and one from column B like a menu. There are literally thousands of entanglement experiments, and they each explore a different idea around entanglement. So you must be specific to make good sense.

http://www.thenakedscientists.com/HTML/science-news/news/2445/

I want to entangle solid objects. Which I can using only beam splitters and detectors according to this

Next came the entanglement, which they achieved by setting up a beam-splitter and detectors. They fired two laser pulses at each diamond, 350 femtoseconds apart. The second pulse picked up the energy the first pulse left behind before reaching the detector as an especially-energetic photon. If the system were classical, the second photon should pick up extra energy only half the time – only if it happened to hit the diamond where the energy was deposited in the first place.

Schematic of the experimental layout for generating entanglement between two diamonds. A pump pulse is split by the beamsplitter BS and focused onto two spatially separated diamonds. Optical phonons are created by spontaneous Raman scattering, generating the orthogonally polarized heralding Stokes fields sL, sR [see inset (A): |n〉 represents phonon number states in diamond]. Polarization beamsplitter PBS1 combines the spatial paths, and the half-wave plate HWP rotates and mixes the fields on PBS3, which are then directed into the single-photon detector Ds. A probe pulse, with programmable delay, coherently maps the optical phonon into the orthogonally polarized anti-Stokes fields aL, aR [see inset (A)], which are similarly combined and mixed on PBS2 and PBS4, and detected on the detectors Da+, Da−. The relative phase ϕa between the fields aL,R is controlled by a sequence of quarter- and half-wave plates (18). Rejected pump beams from PBS1,2 are used to stabilize the interferometer. Displacements of neighboring atoms from their equilibrium positions are anticorrelated in the optical phonon mode [see inset (B)], with a vibrational period of 25 fs in diamond. Inset (C) shows one of the diamond samples, with a coin for scale.

 

[sciencejournalist00]

Experimental set-up. Each nitrogen–vacancy (NV) centre resides in a synthetic ultrapure diamond oriented in thedirection. The two diamonds are located in two independent low-temperature confocal microscope set-ups separated by 3 m. The NV centres can be individually excited resonantly by red lasers and off-resonantly by a green laser. The emission (dashed arrows) is spectrally separated into an off-resonant part (phonon sideband, PSB) and a resonant part (zero-phonon line, ZPL). The PSB emission is used for independent single-shot readout of the spin qubits9. The ZPL photons from the two NV centres are overlapped on a fibre-coupled beamsplitter. Microwave pulses for spin control are applied via on-chip microwave striplines. An applied magnetic field of 17.5 G splits the mS = ±1 levels in energy. The optical frequencies of NV B are tuned by a d.c. electric field applied to the gate electrodes (inset, scanning electron microscope image of a similar device). To enhance the collection efficiency, solid immersion lenses have been milled around the two NV centres. (Credit: H. Bernien et al./Nature)

 

[sciencejournalist00]

Yes, no one is disputing that for polarization entangled states. As I say, you are mixing and matching ideas that you are reading that have similar words. You must realize that each experiment is unique and presents its own elements. You can't take one from column A and one from column B like a menu. There are literally thousands of entanglement experiments, and they each explore a different idea around entanglement. So you must be specific to make good sense.

http://www.nature.com/news/diamond-shows-promise-for-a-quantum-internet-1.12870
To entangle qubits in separate pieces of diamond, the team uses lasers to entangle each qubit with a photon at temperatures of 10 kelvin. The photons meet midway through a fibre-optic cable, where they are themselves entangled.

A quantum Internet would use entangled photons traveling down fibre-optic cables to in turn entangle qubits, with the aim of one day providing super-secure communications, or delivering software and data to future quantum computers

 

[DrChinese]

Experimental set-up. Each nitrogen–vacancy (NV) centre resides in a synthetic ultrapure diamond oriented in thedirection. The two diamonds are located in two independent low-temperature confocal microscope set-ups separated by 3 m. The NV centres can be individually excited resonantly by red lasers and off-resonantly by a green laser. The emission (dashed arrows) is spectrally separated into an off-resonant part (phonon sideband, PSB) and a resonant part (zero-phonon line, ZPL). The PSB emission is used for independent single-shot readout of the spin qubits9. The ZPL photons from the two NV centres are overlapped on a fibre-coupled beamsplitter. Microwave pulses for spin control are applied via on-chip microwave striplines. An applied magnetic field of 17.5 G splits the mS = ±1 levels in energy. The optical frequencies of NV B are tuned by a d.c. electric field applied to the gate electrodes (inset, scanning electron microscope image of a similar device). To enhance the collection efficiency, solid immersion lenses have been milled around the two NV centres. (Credit: H. Bernien et al./Nature)

And after reviewing the above diagram, your conclusion is that the PBS is the only thing necessary to create entanglement. I am sure that would be news to a few scientists.

 

[DrChinese]

A quantum Internet would use entangled photons traveling down fibre-optic cables to in turn entangle qubits, with the aim of one day providing super-secure communications, or delivering software and data to future quantum computers

I think this general concept is known to quite a few people. I would again ask: what is your remaining question? Everything else you have has been answered.

 

[sciencejournalist00]

Why do you bother buying expensive nonlinear crystals with very low conversion efficiency when you can use beam splitters and when momentum conservation which leads to pair production is found in very many phenomena? Even collisions will make the direction and momentum of one particle depend on the other particle, you do not need actual particle decay in radioactivity and spontaneous parametric down conversion

Why choose expensive ways instead of cheap ways?

 

[Nugatory]

Why choose expensive ways instead of cheap ways?

There are two plausible answers to that question.
1) The scientists doing the experiment are stupid.
2) The cheap way that you're thinking of doesn't work because quantum mechanics doesn't work the way you think it does.

In this case, the answer is #2. If you want to learn QM, Physics Forums is one of the places outside of an academic setting where you can find expert help... But arguing is an ineffective way of learning, so this thread is closed.