Four-Photon Entanglement: Is a "Pure" State Possible?

[DrChinese]

It is possible to entangle more than 2 photons. A common configuration is to entangle 4 photons, with a common situation as per the following:

Experimental observation of four-photon entanglement from down-conversion

in which the state is described as (figure 1 of the reference):

sqrt(1/3) (|HHVV> + |VVHH> −
1/2 (|HVHV> − |HVVH> − |VHHV> + |VHVH>)
)

I.e. there is an interference term and you don't see a pure expression such as HHHH + VVVV or similar.

So here is my question: can a "pure" state be created with photons where there are more than 2 photons? Could the following configuration - theoretically - be created?

|HHH> + |VVV>

I think you could do some interesting experiments if you could create that state. Just wondering if anyone knew about this.

Thanks,

-DrC

 

[Meir Achuz]

The three photons from triplet positronium decay are entangled.

 

[f95toli]

It is possible, states with 3 or more entangled photons are known as a GHZ states and you should be able to find more information about this using e.g. Google Schoolar.
Entangled photons are usually generated via PDC and beam-splitters and are therefore created in pairs. However, it is possible to start with 2 pairs and then simply use one photon as a "trigger" which leaves 3 entangled photons.

It guess it might also be possible to create 3 entangled photons using a single photon source+delay lines but I don't know if anyone has ever tried that.

 

[Galileo]

That's just a three qubit GHZ-state right? I`m quite positive they have been created and have used to grossly violate Bell inequalities even more than 2-qubits would.

I don't have access to online journals right now, but I think this may be of interest to you:
Nature 403, 515-519 (3 February 2000)

Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement

Jian-Wei Pan, Dik (sic) Bouwmeester, Matthew Daniell, Harald Weinfurter & Anton Zeilinger

 

[DrChinese]

The three photons from triplet positronium decay are entangled.

Meir,

Do you know if they end up in a state such as the following (2 terms):


|HHH> + |VVV>


I know my question was not clear. I realize that photons can be entangled in groups larger than 2... but those types of setups always seems to have a lot of terms (usually 4 or more). I am looking for something in which the relationship between all of the photons is binary... H or V in any rotated direction.

 

[physicsbhelp]

it is possible.

 

[DrChinese]

That's just a three qubit GHZ-state right? I`m quite positive they have been created and have used to grossly violate Bell inequalities even more than 2-qubits would.

I don't have access to online journals right now, but I think this may be of interest to you:
Nature 403, 515-519 (3 February 2000)

Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement

Jian-Wei Pan, Dik (sic) Bouwmeester, Matthew Daniell, Harald Weinfurter & Anton Zeilinger

I am familiar with this work, but they create 3 photon sets that have 4 terms and not 2. In other words, you don't know if the polarizations are all the same or not because the state is something like:

|H'H'H'> + |H'V'V'> + |V'H'V'> + |V'V'H'>

Whereas I am looking for:

|H'H'H'> + |V'V'V'>

In this state, a measurement of one guarantees you knowledge of the other 2 photons.

 

[Meir Achuz]

Meir,

Do you know if they end up in a state such as the following (2 terms):


|HHH> + |VVV>

It's not that simple. The entagled polarizations would depend on the angles.
If you told me two polarizations and angles, I could tell you the third.
This case is probably not what you have in mind.

 

[DrChinese]

It's not that simple. The entagled polarizations would depend on the angles.
If you told me two polarizations and angles, I could tell you the third.
This case is probably not what you have in mind.

I was thinking of this case:

With 2 PDC photons, you get in any rotated orientation:


Type I:
|HV> + |VH>

Type II:
|HH> + |VV>

Either way, if you know the orientation of one photon, you know with certainty the orientation of the other.

I would like to extend that to N photons, where N>2:

|HHH> + |VVV>

...or something similar like:
|VHH> + |HVV>

The idea would be: If you know the polarization one photon (at any orientation) then you would know the polarization of the other 2 photons at that orientation.

So: if you measured one of the photons at, say, 20 degrees from the vertical, then you would know what to expect for the other 2 photons if they were also measured at 20 degrees. Is there anything/something that prohibits that kind of state from occurring?

 

[RandallB]

What DrC is looking for is not that complex:
In the case of two photons generated in type I PDC you have:
|HH> + |VV> (Instead of the more popular type II |HV> + |VH> )

When testing the first photon at 30° Bell testing of the second photon at various angles to confirm “entanglement” will give the QM non-linear correlations of:

75 % @ 0° (“V”)
100% @ 30° (or -150°)
75 % @ 60° (or -120°)
50 % @ 75° (or -105°)
25 % @ 90° (“H”)
0 % @ 120° (or - 60°)
etc.

Such results found via Bell testing is the only known experimental confirmation of entanglement.

DrC is asking there exists any experimental verification of three photon entanglement:
|HHH> + |VVV>

Which would mean measuring one of the three at 30° should give the same correlation results as above for either of the other two, without even testing the third.
I assume DrC has in mind discovering more detail about the unrealistic and/or non-local nature of entanglement by following up with detailed correlation observations between all three photons by using a variety third test angles on that third photon.

Don’t know if is even possible; IMO no such three photon entanglement has been shown to date, to even consider such 3 angle testing. Three photon entanglement, experientially confirmed would be a big deal, and would not be a hard paper to find if such experimental results existed.

In the case of triplet positronium decay – I have not seen where anyone has demonstrated predictable knowledge of where the second and third photons would be found relative to a location for the first photon detection.
Without firm knowledge of where the photons would be; I don’t see how polarization correlation testing could even be attempted.

 

[staf9]

Theoretically, it should be possible to entangle any number of photons, right?

 

[RandallB]

Theoretically, it should be possible to entangle any number of photons, right?

No theoretical mechanism I’ve ever heard of.
To qualify as verified observation of entanglement, such a theoretical method should be able to produce 3 or more separate streams of time correlated photons. Testers at 3 or more “space like” separated areas would need to be able to randomly select tests from ANY TWO detection areas and produce “entanglement” results. Those that prepare the photon beams to be detected should have no input into which two beams are acceptable for testing by the observers.

I have seen ideas where they manipulate beam preparation and experimental layout, so that by restricting observers to what kind of testing and which areas can be compared to make something appear to be multi-photon entanglement. But that is a simple form of miss-direction not science; Vegas Magic acts do that sort of thing all the time.

 

[Count Iblis]

Isn't there a CNOT gate for photons?

 

[Count Iblis]

A near deterministic linear optical CNOT gate

 

[ppnl]

It is possible to entangle more than 2 photons. A common configuration is to entangle 4 photons, with a common situation as per the following:

http://arxiv.org/abs/quant-ph/0302042"

in which the state is described as (figure 1 of the reference):

sqrt(1/3) (|HHVV> + |VVHH> −
1/2 (|HVHV> − |HVVH> − |VHHV> + |VHVH>)
)

I.e. there is an interference term and you don't see a pure expression such as HHHH + VVVV or similar.

So here is my question: can a "pure" state be created with photons where there are more than 2 photons? Could the following configuration - theoretically - be created?

|HHH> + |VVV>

I think you could do some interesting experiments if you could create that state. Just wondering if anyone knew about this.

Thanks,

-DrC

Would violate conservation of quantum spin wouldn't it?

Say you have a system with a particular spin. Now it splits into three parts the sum of whose spins equals the spin of the original system. Now if you measure the polarization of each part at a different angle there is no way that any result you get could sum up correctly. I think.

 

[Count Iblis]

You can create any state just like in case of qubits using Hadamard rotations and the Controlled NOT (CNOT) gate.

CNOT with second bit the target bit the first the control bit:

|HH> ----> |HH>

|HV> ----> |HV>

|VH> ----> |VV>

|VV> ----> |VH>

Starting with the state |HHH>, perform Hadamard rotation on the first bit

1/sqrt(2)[|H> + |V>]|HH> =

1/sqrt(2)[|HHH> + |VHH> ]

Now do a CNOT operation with the first bit the control bit and the second the target bit:

1/sqrt(2)[|HHH> + |VVH>]

Finally again a CNOT with the second bit the control bit the third the target bit:

1/sqrt(2)[|HHH> + |VVV>]

 

[RandallB]

You can create any state just ….
…
Starting with the state |HHH>, …….

But the OP question was not what could be done "starting" with |HHH
But if such a state could be created as in; Has anyone ever confirmed such a three or more photon state of “pure entanglement” with “no interference term”?

That would mean satisfying a Bell Theorem experiment by randomly selecting only two of the three or more photons. None of the papers claiming multiple entanglements demonstrate or confirm that kind of pure or complete level of entanglement.