Can (almost) all the properties be entangled

[whatdoido]

Two particles cannot be entangled in respect to position and momentum, I've read. But can particles be entangled by all other properties, including either position or momentum? For example by energy, momentum, spin and polarization (+some other(s)?) between two photons. I've read in some other threads that more than one property can be entangled, so I guess almost all properties can be entangled. In any case, how can those correlations be experimentally shown, does not measuring one property break the entanglement. Or do other properties stay entangled even then?

 

[mfb]

Two particles cannot be entangled in respect to position and momentum, I've read.

Where did you read that?
It depends on what exactly is meant with "entangled in respect to position and momentum".

There is nothing fundamental which would prevent entanglement. Some combinations might be hard to impossible to prepare experimentally, however.

In any case, how can those correlations be experimentally shown, does not measuring one property break the entanglement.

Prepare many systems, measure correlations between measurements.

 

[whatdoido]

Where did you read that?

Here for example: http://physics.stackexchange.com/qu...ent-to-defy-heisenbergs-uncertainty-principle
Or did I misunderstand it?

It depends on what exactly is meant with "entangled in respect to position and momentum".

Particle A would have the same position and momentum as particle B when measured, but would not this violate uncertainty principle.

There is nothing fundamental which would prevent entanglement. Some combinations might be hard to impossible to prepare experimentally, however.

Maybe I worded my question poorly or I did not understand your comment. But I meant can a particle have the whole combination of properties entangled with respect to other particle. All possible properties. Like measuring spin and showing correlation. Measuring polarization and showing correlation. Measuring everything and showing correlation. These measurements between two particles. Probably experimentally impossible then, but how about theoretically? Or maybe I did not understand that you did answer to my question and there is nothing fundamental to make it impossible.

 

[ZapperZ]

Two particles cannot be entangled in respect to position and momentum, I've read.

You will learn, in this forum, that this is not adequate as a source. You must clearly cite your sources for us to evaluate if you're reading it correctly, or if you're given a wrong information.

But can particles be entangled by all other properties, including either position or momentum? For example by energy, momentum, spin and polarization (+some other(s)?) between two photons. I've read in some other threads that more than one property can be entangled, so I guess almost all properties can be entangled. In any case, how can those correlations be experimentally shown, does not measuring one property break the entanglement. Or do other properties stay entangled even then?

There is a different between particles all being entangled, versus our ability to detect and measure such entanglement. When If A and B started off being entangled with each other via a property, then if B collided into C, that first entanglement can no longer be that apparent, even if there is a certain degree of connection. Now, imagine if B collided with D, E, F, etc... each subsequent interaction will further dilute any information we had about the original entanglement.

So while, in principal, B might still carry some, miniscule info about A, you will be hard-pressed to justify your claim that A is entangled with B and that we can detect that. And when you have a gazillion particles all interacting with each other, how do you detect something that has thermalized to equilibrium?

Zz.

 

[ZapperZ]

Here for example: http://physics.stackexchange.com/qu...ent-to-defy-heisenbergs-uncertainty-principle
Or did I misunderstand it?

Gosh, using another forum as a source, and much less, the physics stackexchange, is really dubious. Why not use this forum as a source?

You really ought to use proper sources to learn stuff from, not from something like this.

Zz.

 

[whatdoido]

Gosh, using another forum as a source, and much less, the physics stackexchange, is really dubious. Why not use this forum as a source?

You really ought to use proper sources to learn stuff from, not from something like this.

Zz.

Well, I usually use this forum (I lurk a lot) and other good sites as source. I honestly did not know that physics stackexchange had such reputation, the answer there just seemed to be written someone knowledgeable.. I know this area or physics needs years of studying to even to understand the basics, so sometimes reading threads is quite helpful. But I take your advice and no more using physics stackexchange.

Anyway, I also read about this stuff in this forum, for example in this thread https://www.physicsforums.com/threa...gled-on-more-than-one-property-factor.613420/

 

[atyy]

Here for example: http://physics.stackexchange.com/qu...ent-to-defy-heisenbergs-uncertainty-principle
Or did I misunderstand it?

There are two different types of uncertainty principles. The usual one in textbooks has nothing to do with simultaneous measurement of non-commuting observables.

The entanglement described in the Stack Exchange post can validly be used to "simultaneously measure non-commuting observables with perfect accuracy" in a certain sense, eg:

"On the other hand, one of the variations of the Eeinstein-Podolsky-Rosen (EPR) argument [6] runs as follows. In the EPR state of two particles, I and II, the momentum of particle I can be measured by directly and locally measuring the momentum of particle II taking into account the EPR correlation; this follows from the EPR original argument stating that the locality of measurement ensures that the predicted correlation determines the value of momentum of particle I. The locality of the momentum measurement of particle II also concludes that it does not disturb the particle I, and hence we can simultaneously measure the position of particle I by a direct measurement on particle I. Thus, the momentum and position of particle I are simultaneously measurable, so that both the measured values corresponds to elements of reality." http://arxiv.org/abs/0911.1147 [bolding by me]

"Let us discuss them briefly: in the EPR setup, one particle works as a probe, but the two particles are initially correlated. Thus the hypothesis that system and probes are initially uncorrelated is violated. Furthermore, due to this limitation, the EPR scheme does not work for any initial state of the system." http://arxiv.org/abs/1212.2815 [bolding by me]

So to formulate a quantitative inequality for simultaneous measurement requires different ideas that the ones used to derive the textbook inequality, and depending on terminology one may say that entanglement allows an uncertainty principle to be violated. There is a lot of controversy about terminology, but if you read all the papers carefully, the disagreement is purely semantic, the physics in all the "opposing" papers is consistent.

 

[jfizzix]

Two particles cannot be entangled in respect to position and momentum, I've read. But can particles be entangled by all other properties, including either position or momentum? For example by energy, momentum, spin and polarization (+some other(s)?) between two photons. I've read in some other threads that more than one property can be entangled, so I guess almost all properties can be entangled. In any case, how can those correlations be experimentally shown, does not measuring one property break the entanglement. Or do other properties stay entangled even then?

Two particles can indeed be entangled in position and momentum.

I have done a good amount of theoretical and experimental work on just such pairs of particles. See for example (PRL 110, 130407 (2013)) and (PRL 92, 210403 (2004)). In particular, pairs of photons generated in the process known as spontaneous parametric downconversion are entangled in the position-momentum degree of freedom.

There is no a priori restriction on what observables of a pair of particles can be entangled.

Indeed, a pair of particles may be entangled in position and in polarization.
Simultaneous entanglement of multiple degrees of freedom is called hyper entanglement.

In addition, different degrees of freedom may be entangled with each other.
For example, the polarization degree of freedom of one particle may be entangled with the position-momentum degree of freedom of another particle.
Entanglement between disparate degrees of freedom is called hybrid entanglement.

One of the simplest ways to show that a pair of particles is entangled in position and momentum is to show that their joint position and joint momentum statistics are so strongly correlated that they demonstrate the EPR paradox. The papers I referenced earlier are particular demonstrations of position-momentum entanglement in this way. Similarly strong correlations can be used to witness entanglement between any pair of degrees of freedom (see, for example Phys. Rev. A 87, 062103 (2013).)

Note: in those papers, Einstein-Podolsky-Rosen steering inequalities, are like Bell inequalities, but violating them just witnesses entanglement by demonstrating the EPR paradox. Also, that 2004 paper is before my time, but very good nonetheless.

Second Note: Strong measurements do break entanglement. In order to witness the entanglement of a pair of particles, we make many identically prepared such pairs, and do measurements on them to see what their statistics are. Assuming that these statistics apply to anyone of the pairs we measure, we can then say we witness its entanglement.