Clarifying entanglement and complimentarity

[San K]

I am trying to integrate the following concepts and don't fully understand it:

entanglement, interference, complimentary (two photon vs one photon), uncertainty principle

Perhaps a faq could be made

Below are a set of question and statements please answer/modify/correct where required.

1. Entangled particles don't have single particle interference
however
2. Entangled particles can interfere with each other

3. One photon and two-photon interference is complimentary

as you increase the degree of entanglement, the degree of single particle interference decreases4. In other words, if you have two entangled particles A & B

then the more coherent A is with itself, the less coherent (and hence less entangled) A is with B

5. Entangled particles are always coherent with each other (A is in coherence with B)

6. how does uncertainty principle relate with entanglement?

7. What does coherence within a single particle/photon mean? does it mean the waves (from the photon) that are traveling the various paths --- are all in phase?

8. Single photon interference is known as 2nd order interference (as long as it's entangled with another photon (?))

9. Two- photon (also known as entangled photon) interference is called - forth order interference.

10. In layman terms, roughly speaking:

if you are entangled...

you cannot be self-coherent, but you are coherent wrt the other photon

if you are not entangled...

its possible to be self-coherent (and hence have self-interference)
and
also coherent with some other particle/photon
but then, you are not entangled

 

[jfizzix]

I am trying to integrate the following concepts and don't fully understand it:

entanglement, interference, complimentary (two photon vs one photon), uncertainty principle

Perhaps a faq could be made

Below are a set of question and statements please answer/modify/correct where required.

1. Entangled particles don't have single particle interference
however
2. Entangled particles can interfere with each other

3. One photon and two-photon interference is complimentary

as you increase the degree of entanglement, the degree of single particle interference decreases


4. In other words, if you have two entangled particles A & B

then the more coherent A is with itself, the less coherent (and hence less entangled) A is with B

5. Entangled particles are always coherent with each other (A is in coherence with B)

6. how does uncertainty principle relate with entanglement?

7. What does coherence within a single particle/photon mean? does it mean the waves (from the photon) that are traveling the various paths --- are all in phase?

8. Single photon interference is known as 2nd order interference (as long as it's entangled with another photon (?))

9. Two- photon (also known as entangled photon) interference is called - forth order interference.

10. In layman terms, roughly speaking:

if you are entangled...

you cannot be self-coherent, but you are coherent wrt the other photon

if you are not entangled...

its possible to be self-coherent (and hence have self-interference)
and
also coherent with some other particle/photon
but then, you are not entangled

1.) Perfectly entangled particles exhibit no single particle interference. Partially entangled particles can exhibit partial single particle interference (partial coherence).

2.) Entangled particles can indeed interfere with each other. A nice example of this in Hong-Ou-Mandel interference in pairs of entangled photons.

3.) One and two-photon interference does exhibit a tradeoff, where a larger amount of entanglement means a smaller amount of single particle interference. I'm not sure what calling it complementarity really means, though.

4.) Yes, the more coherent the state of A is, the less it can be entangled with another particle B. This is known as the monogamy of entanglement. If A were a perfectly coherent pure state, it could not be entangled with anything else because it could not even be correlated with anything else.

5.) I'm not sure what this question is asking. If A and B are entangled, you can perform quantum interference experiments that would yield results that unentangled pairs can not provide.

6.) The uncertainty principle and entanglement are both rooted in the foundations of quantum mechanics, in particular, in the superposition principle. The superposition principle says that the proper representation of the state of a quantum system is as a sum over basis states, like components of a vector in a particular coordinate system. The uncertainty principle comes from the fact that there's no basis in which all of the observables of a system are well-defined. Quantum entanglement comes from extending the superposition principle to pairs or groups of quantum systems.

7.) Theoretically, one can speak about the coherence in the state of a single system, like the coherence in waves in general. If a set of waves are coherent, they have a fixed phase relationship with one another. Experimentally, we never measure only a single particle, we measure many particles in order to figure out the probability distributions of what we are trying to measure.

8.) Second order interference (coherence) is called such because it is second order in the electric field; it is related to the average product of the electric field in two different locations and/or times.

9.) Two photon interference is called fourth order interference because it depends on the product of intensities, or on the fourth power of the electric field at different locations and times. I would recommend looking at Rodney Loudon's "The Quantum theory of light" for a more detailed description.

10.) It is possible to be partially entangled. weakly entangled pairs of photons can exhibit partial one-photon coherence and partial two-photon coherence. They cannot exhibit strong coherences of both types, though.

 

[San K]

well answered, thanks jfizzix.

10.) It is possible to be partially entangled. weakly entangled pairs of photons can exhibit partial one-photon coherence and partial two-photon coherence. They cannot exhibit strong coherences of both types, though.

this is what I meant by complementarity, in 3) above.

like time & energy
position & momentum etc.

could all the complementarities boil down to some single fundamental fact of nature?

6.) The uncertainty principle and entanglement are both rooted in the foundations of quantum mechanics, in particular, in the superposition principle. The superposition principle says that the proper representation of the state of a quantum system is as a sum over basis states, like components of a vector in a particular coordinate system. The uncertainty principle comes from the fact that there's no basis in which all of the observables of a system are well-defined. Quantum entanglement comes from extending the superposition principle to pairs or groups of quantum systems.

Well said!

 

[jfizzix]

In this sense, I expect complementarity arises again from the fact that there is no basis in which all measurements have well-defined outcomes.

I jumped at this question because I do research into entanglement as a PhD student.

 

[San K]

In this sense, I expect complementarity arises again from the fact that there is no basis in which all measurements have well-defined outcomes.

Agreed.

I jumped at this question because I do research into entanglement as a PhD student.

Good. Look forward to more interactions on this forum.