Can you locally tell that a measurement you made was entangled?

[PAllen]

TL;DR Summary

You can't do FTL message sending via entanglement, but can you tell whether you have measured an entangled particle without being told?

Suppose you make a measurement of some particle. If you know it is entangled, you may have conditional knowledge of measurements that might be made at a spacelike distance (if the other observer does/has done x, they will/did get result y). Note, I am using local in the sense of special relativity - a small volume of spacetime in which some measurement has been made, not in the sense of Bell.

So my question is: If you know someone is setting up a series of identical preparations, but you don't know whether the setup entangles two particles or not (whichever it is, it is the same for all cases - they are identical preparations), can you tell whether the particles are entangled by a series of local measurements with no communication outside of your small world tube? This is not the same as getting information FTL, just knowing whether you have measured an entangled pair member without being told.

 

[phinds]

This is not the same as getting information FTL,

Yes, it is, so no you can't.

EDIT: oh, wait ... I was wrong (or at least my reasoning for giving that response was wrong). I tried to explain how that could result in FTL communication but ended up seeing how I was mistaken. I still don't think you can tell, but my particular logic was wrong.

 

[martinbn]

I think you cannot tell.

 

[PeroK]

Summary: You can't do FTL message sending via entanglement, but can you tell whether you have measured an entangled particle without being told?

Suppose you make a measurement of some particle. If you know it is entangled, you may have conditional knowledge of measurements that might be made at a spacelike distance (if the other observer does/has done x, they will/did get result y). Note, I am using local in the sense of special relativity - a small volume of spacetime in which some measurement has been made, not in the sense of Bell.

So my question is: If you know someone is setting up a series of identical preparations, but you don't know whether the setup entangles two particles or not (whichever it is, it is the same for all cases - they are identical preparations), can you tell whether the particles are entangled by a series of local measurements with no communication outside of your small world tube? This is not the same as getting information FTL, just knowing whether you have measured an entangled pair member without being told.

If you make a measurement on a set of particles, you will get a distribution that depends on the state of the particle; or, on the state of a two-particle entangled system. What you can deduce from the data all depends on the knowldege of the preparation process.

For example, if you prepare a set of spin 1/2 particles that are all spin up in a certain direction, then a measurement of spin in that direction will always return spin-up. So, you would know that you are not receiving a random particle from a zero-total-spin entangled pair.

But, of course, the particle you measure may be entangled in some other way. In general, it is entangled with the apparatus that produced it. From that perspective, the question makes no sense.

So, it really boils down to what sort of entanglement you think you are looking for, and what options there are for particle preparation that you are trying to decide between.

 

[DrChinese]

So my question is: If you know someone is setting up a series of identical preparations, but you don't know whether the setup entangles two particles or not (whichever it is, it is the same for all cases - they are identical preparations), can you tell whether the particles are entangled by a series of local measurements with no communication outside of your small world tube? This is not the same as getting information FTL, just knowing whether you have measured an entangled pair member without being told.

AFAIK the answer is NO. Obviously, the particle you get will be in a superposition of states if it is entangled. And therefore must also be in a superposition of states if it is not entangled, unless you want that to be the identifying difference/characteristic. So if they are both in a similar superposition when you get them, then they should be indistinguishable as to entangled vs. unentangled. Every outcome is random.

 

[DarMM]

Wouldn't the local state of any member of an entangled pair be some density matrix $\rho$ and thus be equivalent to some local preparation. Thus no.

 

[kith]

As others have said, you can't do it by acting only locally.

If you have unitary control over the combined system, you can detect the presence of correlations by measuring only locally if you compare situations with different global time evolutions (see Gessner et al. 2014). But note that this not only requires global unitary control but also local state tomography, i.e. you can't make the inference for a single instance but need to have many identical preparations.

 

[PAllen]

As others have said, you can't do it by acting only locally.

If you have unitary control over the combined system, you can detect the presence of correlations by measuring only locally if you compare situations with different global time evolutions (see Gessner et al. 2014). But note that this not only requires global unitary control but also local state tomography, i.e. you can't make the inference for a single instance but need to have many identical preparations.

Fascinating paper. To me, that means the answer to what I really wanted to know is yes. I was insufficiently creative in posing the question. I was wondering because I couldn’t think of any causality based argument prohibiting it, and I had recently seen all these entanglement transfer ideas here (on PF) that were completely new to me, so I wondered if someone had come up with a clever way to do this. This being distinguish an entangled particle state from one that is identical except for entanglement, with local measurements and no outside communication. It seems to me, that under the right circumstances, that is exactly what the method in this paper accomplishes.

Thanks!

Thanks also to others who explained why it could never be done with a single local measurement.

 

[vanhees71]

Again, I would caution against trying to answer such vaguely posed questions. You need to specify concretely each case of an experiment (or gedanken experiment for that matter), i.e., in which state the two-particle system is prepared and what then is measured (on an ensemble of so prepared two-particle systems).

In this generality it's hard to answer, but what's for sure is that within relativistic microcausal QFT there's from first principles no way to learn from local measurements anything about space-like separated events. Formally that's seen from the fact that the S-matrix obeys the linked cluster principle for any such constructed theory.

Knowing however about the preparation of the two-particle system in an entangled state you know which correlations of local measurements on either of the two particles are to be expected and which measurement you have to make. E.g., you must be sure to check the correlations with local meaasurements at distant places of only the really entangled particle pairs. This usually is achieved by taking proper timing information with the measurement events. E.g., in the typical Bell tests with entangled photons you make two-photon coincidence measurements with photo dectectors at far distant places. Having only one entangled photon pair at a time you can be sure to always check correlations on only the entangled pairs and not some random two photons (of course all this within the accuracy you can achieve with your given setup concerning both the preparation of the entangled photon pair and the measurement devices used to register the photons).

 

[PAllen]

In this generality it's hard to answer, but what's for sure is that within relativistic microcausal QFT there's from first principles no way to learn from local measurements anything about space-like separated events. Formally that's seen from the fact that the S-matrix obeys the linked cluster principle for any such constructed theory.

The question I was asking had nothing to do with knowing about spacelike separated events. An analogy is you know someone is sending you either electrons or positrons, but you don't know which. Trivially this is answerable. In my case, you know someone is sending a series of particles all of which are either entangled with another particle at long distance (by the time you get yours), or are not so entangled. The state of the particles you get are to be identical except for the presence or absence of this entanglement. Your job is determine whether such entanglement is present (you do NOT need to find out about any correlations). That is, all you are trying to do is deduce one final preparation detail the preparer could have sent you but didn't.

The paper provided by @kith suggests this is possible, but not by any series of single measurements of each particle received. Instead, you do a special form of partial cloning, then monitor the evolution the two particles. Over time, and many repeats, you should be able to determine whether you have been sent particles entangled with a distant partner, or not. At least, that is what I get from the paper.