Understanding GHZ Entanglement

In summary, the conversation discusses the concept of three-photon entanglement and how the polarization of one photon affects the other two. There is confusion about whether the other two photons take on the same polarization as the first one or the opposite. The solution is to write the states in terms of |45> and |135> and expand using the distributive property. It is also noted that odd numbers of |45> do not occur in these combinations.
  • #1
StevieTNZ
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878
Hi there,

I was looking through Zeilinger's "Dance of the Photons" where I re-read the section of three-photon entanglement. If one photon is measured in H polarisation, the other two take on H - likewise with V polarisation.

What I find interesting is if we measure one photon and its H polarisation, another (delayed) at 45 degrees, and the last at vertical - when the first photon takes on H polarisation, don't the other two? So when the last photon meets the V polarised filter, shouldn't it fail? But according to GHZ results, it should be vertical.

So the other two photons are NOT in H polarisation when the first one meets the polariser? Or the first photon is NOT in H polarisation - evolves as a superposition in accord with Scrodinger equation (no collapse occurs).

Unless I've mis-understood something?
 
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  • #2
I see where I have mis-interpretated it. The author doesn't make it clear under the diagram he is measuring in another polaristion direction before the photon becomes V or H polarised. v' h' and all that stuff just makes it more confusing.
 
  • #3
If we have the GHZ state: |V>|H>|H>|V> + |H>|V>|V>|H>, if photons 1 and 4 take on polarisation 135, do photons 2 and 3 take on the opposite - 45 polarisation?
 
  • #4
StevieTNZ said:
If we have the GHZ state: |V>|H>|H>|V> + |H>|V>|V>|H>, if photons 1 and 4 take on polarisation 135, do photons 2 and 3 take on the opposite - 45 polarisation?
To find the answer to this, all you need to do is write |H> and |V| in terms of |45> and |135>.
 
  • #5
So replace |H> with |45> and |V> with |135> ?

Because expanding |H> to include |45> and |135>, I'm not sure if they have to match (i.e. with the other |H>)
 
  • #6
StevieTNZ said:
So replace |H> with |45> and |V> with |135> ?

Because expanding |H> to include |45> and |135>, I'm not sure if they have to match (i.e. with the other |H>)
No, write |H> and |V> as linear combinations of |45> and |135>. Each of them will have an expression that's something like (1/√2)(|45>+|135>). I don't remember the exact expressions off the top of my head.
 
  • #7
So |45>|135>|135>|45> + |135>|45>|45>|135> ?
 
  • #8
StevieTNZ said:
So |45>|135>|135>|45> + |135>|45>|45>|135> ?
No, that's not how it's done.
 
  • #9
How is it done? Do photons 1 and 4 share the same polarisation, likewise with 2 and 3? (e.g. in |H>|V>|V>|H>).

Do we expand it as |45>|45>|45>|45>+|45>|135>|135>|45>+|135>|45>|135>|135> etc.?
 
  • #10
StevieTNZ said:
Do we expand it as |45>|45>|45>|45>+|45>|135>|135>|45>+|135>|45>|135>|135> etc.?
Yes, that's how it's done. We write |H> and |V> in terms of |45> and |135>, and so we expand the whole quantum state as a sum of products like |45>|45>|45>|45>.
 
  • #11
"Combinations with odd numbers of |45> do not occur".

But you can write those from |V>|H>|H>|V>+|H>|V>|V>|H>?
 
  • #12
StevieTNZ said:
"Combinations with odd numbers of |45> do not occur".

But you can write those from |V>|H>|H>|V>+|H>|V>|V>|H>?
I told you, just write |H> and |V> in terms of |45> and |135>. Then just expand out the products using the distributive property, like |45>(|45>+|135>)=|45>|45>+|45>|135>
 

1. What is GHZ Entanglement?

GHZ Entanglement is a phenomenon in quantum mechanics where multiple particles become correlated and share a single, unified state. This means that the particles are connected in such a way that the state of one particle depends on the state of the other particles, even if they are physically separated.

2. How does GHZ Entanglement work?

GHZ Entanglement occurs when a group of particles are prepared in a specific quantum state, such as the GHZ state. This state is a superposition of all possible states for the particles, meaning they exist in all possible states simultaneously. When one particle is measured, its state becomes well-defined, and the states of the other particles are also determined instantaneously, regardless of the distance between them.

3. What is the significance of GHZ Entanglement?

GHZ Entanglement is significant because it demonstrates the non-local nature of quantum mechanics, meaning that particles can be connected and influence each other's states even when they are separated by large distances. This phenomenon has potential applications in quantum communication, cryptography, and computing.

4. How is GHZ Entanglement measured and verified?

GHZ Entanglement can be measured and verified using various methods, including Bell inequality tests and quantum state tomography. These methods involve measuring the correlations between the particles and comparing them to the predictions of quantum mechanics. If the results match, it confirms the presence of entanglement.

5. What are the challenges in understanding GHZ Entanglement?

One of the main challenges in understanding GHZ Entanglement is the counterintuitive nature of quantum mechanics. The concept of particles being connected and influencing each other's states can be difficult to grasp, and it goes against our everyday experience. Additionally, there are technical challenges in preparing and maintaining entangled states, which require precise control and isolation from external influences.

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