Entanglement swapping, monogamy, and realism

[PeterDonis]

The only possible difference is that Fuchs and Peres are also willing to talk about the likelihood of single events

I believe their approach to probabilities is Bayesian, which treats probabilities as states of epistemic belief and so has no problem assigning probabilities to single events.

 

[gentzen]

*By minimalist I am referring to the account of QM presented by Fuchs and Peres in articles like this one https://physicstoday.scitation.org/doi/pdf/10.1063/1.883004

This seems to be more or less the interpretation that @vanhees71 is using.

I think so too. The only possible difference is ...

No, just no. This is NOT the minimal statistical interpretation. And this is not close to vanhees71's usage of the minimal statistical interpretation either.

 

[DrChinese]

... Locality is readily preserved.

*By minimalist I am referring to the account of QM presented by Fuchs and Peres in articles like this one https://physicstoday.scitation.org/doi/pdf/10.1063/1.883004

Quantum theory is inherently nonlocal, although signal locality is respected. You - as many - have formulated requirements for some definition of nonlocality that cannot be met. Specifically, you basically reject experimental nonlocality proofs which some central observer does not experience until all of the information arrives - which is limited by signal. Circular reasoning - you have proved what you assume.

What is clearly nonlocal, as we have discussed here: An experimentalist here can create - or not - a distant biphoton from components that have never existed in a common light cone. There really is no disputing this experimental fact as I have characterized it. If you choose to reject this because it does not demonstrate signal nonlocality, that's... circular.

Logically, if there is something called "quantum nonlocality" (as I say there is) and it can be demonstrated (as it can be), but it does not feature FTL signaling: then it cannot be judged by a "macroscopic" experiment where component results must be brought together before you accept the nonlocality. Macroscopic Alice can write her results down and compare them with the measurement results of Macroscopic Bob and Victor anytime. Obviously, their combined story indicates that there is quantum nonlocality. You can't wave your hands and ignore the obvious.

Well, I guess you can...

 

[Morbert]

No, just no. This is NOT the minimal statistical interpretation. And this is not close to vanhees71's usage of the minimal statistical interpretation either.

Dreischner calls the account of Peres + Fuchs a minimal instrumentalist interpretation and cites Friebe (though I do not have access to the cited text). By minimal statistical interpretation, do you mean a minimal ensemble interpretation? I don't know if they are as different as you imply, but the minimal interpretation as described in this thread and others has an instrumentalist character (for example, the association of a quantum state with a preparation procedure). If there is some important distinction or misrepresentation then please be explicit.

 

[Morbert]

Quantum theory is inherently nonlocal, although signal locality is respected.

Here you are making a stronger claim that can't be categorised as a difference in interpretation. And it's one I disagree with. E.g. According to decoherent histories interpretations and minimal instrumentalist interpretations, quantum theory is no more nonlocal than classical theory.

 

[Fra]

What is clearly nonlocal, as we have discussed here: An experimentalist here can create - or not - a distant biphoton from components that have never existed in a common light cone.

Sure, but we can also agree the experimenter can not "create this" without information about measurements on other entangled parts of both the components. Ie. The experimebter cant create this without this information. Do we agree?

There really is no disputing this experimental fact as I have characterized it. If you choose to reject this because it does not demonstrate signal nonlocality, that's... circular.

As we use different notions of locality, I'm fine with agreeing with you with that disclaimer.

But that form of nonlocality you refer to is not a problem per see (At least not for me). The notion of locality that is part of the often constructing principles of physics isnt the kind of locality that you speak of. The only problem is that its almost the same word for different things.

/Fredrik

 

[Nullstein]

This is wrong. The "event ready" signal is generated by a combination of things: the 2 & 3 photons arriving at the BSM device within the same narrow time window, and the output of the BSM indicating the particular Bell state that the BSM is set up to distinguish. This happens at the BSM, not at the initial preparation. @DrChinese is more familiar than I am with the specific papers describing the experiments, and I'm sure can give specific references to the descriptions in those papers that match the above.

I don't think the specific details are relevant. The point of the event ready signal is to select those events which can safely be assumed to be successful measurements. This doesn't add anything conceptually new to the analysis of the idealized experiment. You still have a full ensemble of events which constitue successful measurements and you decompose this full ensemble into subensembles according to the measurement result of the BSM.

For our purposes, let's assume that the 1 & 4 measurement systems (PBS plus 2 detectors for each) are positioned such that when we have a successful BSM, the 1 & 4 detectors go off at the same time (within our designated time window). We add fiber cable to make that work out, and we place them at the same spot. Additionally, we do the same with the BSM detector array. We use fiber to adjust the travel time, and route them to the same location as the 1 & 4 detectors. All 4 photons will arrive at location where all of the detectors are, and the photons will all arrive within the same time window. I am adding this little twist so you can see exactly what should be discussed when we talk about an ensemble or subset or subensemble. So what we expect, with a successful BSM, is that 4 detectors will click at almost precisely the same time. For the 1 & 4 photons, each will generate one click indicating their polarization relative to their respective PBS. The BSM detector array will register 2 clicks, one for the 2 photon and one for the 3 photon - but we won't know which is which. So 4 "simultaneous" clicks means we have a successful BSM in this setup.

These events taken together, i.e. prior to post-selection, constitute the full ensemble.

In theory: for every single case where the 1 & 4 photons are detected within the time window: they are entangled.

This sentence makes no sense without saying with respect to which data set you make it. If you consider a dataset consisting of only a single data point, it makes no sense, because the unbiased estimator of covariance is not well defined for a single data point. If you consider the full ensemble, then the statement is false. The photons 1&4 will be uncorrelated in the full ensemble. The statement is true for the post-selected subensembles only.

We may not know which of the 4 Bell states they are in - and therefore we can't perform a Bell test on them - but they ARE entangled. [...] But assuming we are good scientists, there is no subensemble yet.

No. If you don't look at a subensemble, there will not be entanglement in the data. The correlation will be zero. This follows strictly from the math.

 

[Nullstein]

Quantum theory is inherently nonlocal, although signal locality is respected.

You are being imprecise on purpose here. Quantum non-locality means nothing more than the fact that Bell's inequality is violated. What you want to imply is that there are non-local cause and effect relationships. The broad consensus among physicists is that no non-local cause and effect relationship can be inferred from the data. QM can be interpreted either way.

 

[PeterDonis]

I don't think the specific details are relevant.

They most certainly are. Basing the signal on what happens at the BSM is very different from basing it on something from the initial preparation, which is what you said before.

The point of the event ready signal is to select those events which can safely be assumed to be successful measurements.

Not quite. The point of the event ready signal in these experiments is to select those events in which photons 2 & 3 are projected into the particular Bell state that the BSM is set up to uniquely detect. That doesn't mean the other events aren't successful measurements; they're just measurements whose results can't be distinguished by the humans reading the output of the apparatus. But they still involve projecting photons 2 & 3 into a Bell state and everything associated with that (for example, that photons 1 & 4 are also projected into a Bell state).

You still have a full ensemble of events which constitue successful measurements and you decompose this full ensemble into subensembles according to the measurement result of the BSM.

That's not correct for these particular experiments. The "event ready" signal runs are the only runs for which the measurement result of the BSM can be determined. The other runs involve BSM results that the humans reading the apparatus can't distinguish from each other. So the other subensembles can't be picked out. Only the "event ready" subensemble can.

It would be possible in principle to design a more sophisticated BSM that could distinguish all 4 Bell states, so that 4 subensembles could be picked out; but my understanding is that the technical difficulties in doing that in practice have not yet been figured out. In such an experiment, the "event ready" signal would be the arrival of photons 2 & 3 at the BSM within a narrow enough time window for the BSM to act on them at all (if they don't arrive within a narrow enough time window, the BSM does nothing).

 

[Nullstein]

Let me try once more to explain the relationship between correlation and causation and how it applies to entanglement swapping:

Experimentally, we find that certain sets of data show correlation between spacelike separated variables ##A## and ##B##. In general though, correlation does not imply a cause and effect relationship between those variables, i.e. we may not conclude that ##A## caused ##B## or the other way around. Why is that?

1. The correlation may be mediated by a third variable ##C##, i.e. ##C## caused ##A## and ##C## caused ##B##. In that case, the correlation will go away if we condition on the variable ##C##. This is called a common cause explanation. Bell's theorem proves that a common cause explanation for the EPR correlations is excluded.
2. The correlation may arise, because we are only looking at a specific subset of the data. In particular, if we look at data which was obtained by conditioning on a common effect, then inferring causality is forbidden if the correlation goes away after summing over the common effect variable. This is the case in entanglement swapping. Here, the correlation in the subensembles will go away if we sum over the possible measurement outcomes of the BSM, i.e. if we pass to the full ensemble.

If there was still correlation between ##A## and ##B## after we have taken care of these issues, we may indeed infer causality from the fact that ##A## and ##B## are correlated. But in the case of entanglement swapping, it is just a fact that the correlation goes away after taking care of these issues, so we may not infer causality.

All of this is well understood applied statistics. It's not something I made up. This is how causal inference is taught and done in every empirical field of science. The paper https://arxiv.org/abs/1606.04523 shows that this is also well understood in the case of entanglement swapping. Robert Spekkens, one of the authors, is one of the leading researchers in quantum foundation and the application of causal inference to quantum mechanics, so this should certainly be taken seriously.

 

[Nullstein]

They most certainly are. Basing the signal on what happens at the BSM is very different from basing it on something from the initial preparation, which is what you said before.

Fine, if you want to study the more complicated situation, it just means that you are even less allowed to conclude causal relationships from the collected data. It means you need to to perform even more checks of the causal structure and take even more possible causal relationships into account, before any conclusion can be made. If I don't want to discuss these complications, it just means I'm being generous to you.

Not quite. The point of the event ready signal in these experiments is to select those events in which photons 2 & 3 are projected into the particular Bell state that the BSM is set up to uniquely detect. That doesn't mean the other events aren't successful measurements; they're just measurements whose results can't be distinguished by the humans reading the output of the apparatus. But they still involve projecting photons 2 & 3 into a Bell state and everything associated with that (for example, that photons 1 & 4 are also projected into a Bell state).

Well, I agree, but this just means that you need to perform an even more complicated analysis of the experimental setting, before you can perform proper causal inference. So it just got more complicated for you to argue for your position. Me agreeing to discuss the idealized experiment rather than the real world experiment is a generosity, not an excuse.

What you need to do to infer a causal relationship now is to draw a causal diagram and take all the effects into account that I explained in post #150. You then calculate the corrected correlations that account for these effects and you'd have to show that there is still correlation after the effects have bene taken into account.

 

[PeterDonis]

The paper https://arxiv.org/abs/1606.04523 shows that this is also well understood in the case of entanglement swapping.

Where is entanglement swapping discussed in the paper? I see a "swap" operator defined, but I don't see how it relates to what the BSM does in the entanglement swapping experiment we have been discussing.

 

[PeterDonis]

if you want to study the more complicated situation

What more complicated situation? I wasn't comparing two situations, I was correcting your misstatement about the "event ready" signal in the one situation we have been discussing all along.

 

[Nullstein]

Where is entanglement swapping discussed in the paper? I see a "swap" operator defined, but I don't see how it relates to what the BSM does in the entanglement swapping experiment we have been discussing.

The swap gate is a mathematical abstraction of the physical situation in entanglement swapping. It abstractly models the transition that we previously denoted by ##\rho_{1234,\text{before}}\rightarrow\rho_{1234,\text{after}}## in terms of a 4 qubit system. The paper applies to all such swapping experiments, independent of details such as e.g. the temporal and spatial ordering. (As discussed earlier, the temporal and spatial ordering has no effect on the measured statistics, so it can be abstracted away.)

What more complicated situation? I wasn't comparing two situations, I was correcting your misstatement about the "event ready" signal in the one situation we have been discussing all along.

The more complicated situation is what you get if you want to include the events, that did not constitute a proper BSM projection, into the description. In that case, you would need to introduce another variables X = "Has a proper BSM projection occured?" and study the causal graph that includes this variable, taking into account the issues mentioned in #150.

 

[PeterDonis]

It abstractly models the transition that we previously denoted by ##\rho_{1234,\text{before}}\rightarrow\rho_{1234,\text{after}}## in terms of a 4 qubit system.

I only see two qubit systems discussed in the paper.

 

[vanhees71]

I think so too. The only possible difference is that Fuchs and Peres are also willing to talk about the likelihood of single events as well as frequencies of events in ensembles, which I am not sure vanhees is willing to do.

"When we are told that the probability of precipitation tomorrow is 35%, there is only one tomorrow." -- Fuchs and Peres

That's the problem I have with interpretations of probability, no matter whether they are predicted by QT or other means of calculating statistical predictions (e.g., by classical statistical physics), which abandon the "frequentist interpretation", like "QBists".

What does it mean that the probability for rain tomorrow is 35%? Of course there's only one tomorrow, and I can't prepare the wheather situation today many times and check the frequency that it rains or not tomorrow. For me the prediction of some weather model means that at weather condistions like today, experience and/or projections via model simulations, tells me that in 35% of all such cases it will rain. A good statistical analysis also gives a level of significance and an uncertainty of this number, which also is based on experience with such weather models, and then I have some objective estimate for the probability of rain or good weather to plan my barbecue party tomorrow. Of course also this interpretation is after all based on the "frequentist interptation" of the statistical meaning of probabilities. From a single event, you of course can not decide whether your prediction that there's 35% chance for rain tomorrow is a good estimate or not.

 

[mattt]

That's the problem I have with interpretations of probability, no matter whether they are predicted by QT or other means of calculating statistical predictions (e.g., by classical statistical physics), which abandon the "frequentist interpretation", like "QBists".

What does it mean that the probability for rain tomorrow is 35%? Of course there's only one tomorrow, and I can't prepare the wheather situation today many times and check the frequency that it rains or not tomorrow. For me the prediction of some weather model means that at weather condistions like today, experience and/or projections via model simulations, tells me that in 35% of all such cases it will rain. A good statistical analysis also gives a level of significance and an uncertainty of this number, which also is based on experience with such weather models, and then I have some objective estimate for the probability of rain or good weather to plan my barbecue party tomorrow. Of course also this interpretation is after all based on the "frequentist interptation" of the statistical meaning of probabilities. From a single event, you of course can not decide whether your prediction that there's 35% chance for rain tomorrow is a good estimate or not.

Yes, that's what it usually means. The criteria of what exactly "conditions like today" means (among several other things) is what defines the probabilistic method used in each case.

 

[vanhees71]

1&2 are in a Bell state as well as 3&4, i.e., each of these pairs is maximally entangled. There are no correlations between 2&3 or 1&4 in the initial state. I haven't claimed anything like that.

Now if you project to a Bell state of 2&3, in the so prepared subensemble 2&3 are fully entangled, because they are prepared to be in a Bell state. Due to the entanglement of 1&2 and 3&4 this implies that for this subensemble also 1&4 are in a Bell state.

It's a easy, although some elaborate calculation, as described by Jennewein et al in

https://arxiv.org/abs/quant-ph/0201134

It's more easily seen in the 2nd-quantization notation. The four Bell states of a photon pair with momentum labels ##j## and ##k## are created from the Vakuum by
$$\hat{\Psi}_{jk}^{\dagger \pm} \rangle=\frac{1}{\sqrt{2}}[\hat{a}^{\dagger}(\vec{p}_j,H) \hat{a}^{\dagger}(\vec{p}_k,V) \pm \hat{a}^{\dagger}(\vec{p}_j,V) \hat{a}^{\dagger}(\vec{p}_k,H)],$$
$$\hat{\Phi}_{jk}^{\dagger \pm} \rangle=\frac{1}{\sqrt{2}}[\hat{a}^{\dagger}(\vec{p}_j,H) \hat{a}^{\dagger}(\vec{p}_k,H) \pm \hat{a}^{\dagger}(\vec{p}_j,V) \hat{a}^{\dagger}(\vec{p}_k,V)].$$
Then the initial four-photon state can then be written in two forms,
$$|\Psi_{1234} \rangle = \hat{\Psi}_{12}^{\dagger -} \hat{\Psi}_{34}^{\dagger-} |\Omega \rangle,$$
but this can as well be written as
$$|\Psi_{1234} \rangle=\frac{1}{2} (\hat{\Psi}_{23}^{\dagger +} \hat{\Psi}_{14}^{\dagger +} - \hat{\Psi}_{23}^{\dagger -} \hat{\Psi}_{14}^{\dagger -}-\hat{\Phi}_{23}^{\dagger +} \hat{\Phi}_{14}^{\dagger +} + \hat{\Phi}_{23}^{\dagger -} \hat{\Phi}_{14}^{\dagger -})|\Omega \rangle.$$
The former notation shows that photon pairs (12) and (34) are each in the polarization-singlet Bell state but (14) and (23), i.e, are uncorrelated.

The latter notation shows that if you project pair (23) to either of the four Bell state the pair (14) must be found in the same Bell state. In Pan et al's work, which we discuss here, (23) has been projected to the polarization-singlet state, and it has been demonstrated that then also the pair (14) is then in the same polarization-singlet state. This happens with probability 1/4.

Quantum theory is inherently nonlocal, although signal locality is respected. You - as many - have formulated requirements for some definition of nonlocality that cannot be met. Specifically, you basically reject experimental nonlocality proofs which some central observer does not experience until all of the information arrives - which is limited by signal. Circular reasoning - you have proved what you assume.

I don't know, how you can insist on "nonlocality" without clearly telling what you mean by it. It's a mathematical fact that the standard relativistic QFTs (used to formulate the standard model of HEP, which includes also QED, which is the theory describing all quantum-optics experiments) is a local theory, i.e., due to the enforced microcausality conditions on local observables, there are no causal influences between space-like separated events possible, and that's what's usually understood as "nonlocality". This discussion goes again in circles :-(((.

What is clearly nonlocal, as we have discussed here: An experimentalist here can create - or not - a distant biphoton from components that have never existed in a common light cone. There really is no disputing this experimental fact as I have characterized it. If you choose to reject this because it does not demonstrate signal nonlocality, that's... circular.

An experimentalist can create such the biphoton (14) only by projection due to a local measurement on (23), and you have to do coincidence measurements on all four photons. I.e., you need a measurement protocol which enables you to select the subensemble for which (14) is entangled. This is only possible when you bring together the information contained in all measurement protocols in their future light cone. The temporal order of measurements to obtain these measurement protocols is irrelevant, which shows that there's no faster-than-light influence of the projection measurement on (23) on photons 1 and 4 necessary to explain the entanglement of the biphotons in the corresponding subensemble. As @PeterDonis has said above, you can even do the measurement on photons 1 and 4 before you perform the projection of (23) to a Bell state, i.e., by "postselection".

Logically, if there is something called "quantum nonlocality" (as I say there is) and it can be demonstrated (as it can be), but it does not feature FTL signaling: then it cannot be judged by a "macroscopic" experiment where component results must be brought together before you accept the nonlocality. Macroscopic Alice can write her results down and compare them with the measurement results of Macroscopic Bob and Victor anytime. Obviously, their combined story indicates that there is quantum nonlocality. You can't wave your hands and ignore the obvious.

That's a contradiction in it self. If there's no FTL "signalling", i.e., no causal connection between space-like separated events in your model, then your model is not "nonlocal", and standard relativistic QFT is indeed not "nonlocal", as we've discussed zillions of times now.

You can interpret any theory in any way you like. The only restriction is that your interpretation must not contradict the mathematical properties of the model you want to interpret (here it's relativistic QFT).

 

[vanhees71]

I believe their approach to probabilities is Bayesian, which treats probabilities as states of epistemic belief and so has no problem assigning probabilities to single events.

Indeed, but what's the meaning of probabilities for single events? See #156 for further details concerning my question.

 

[Fra]

That's the problem I have with interpretations of probability, no matter whether they are predicted by QT or other means of calculating statistical predictions (e.g., by classical statistical physics), which abandon the "frequentist interpretation", like "QBists".

What does it mean that the probability for rain tomorrow is 35%? Of course there's only one tomorrow

For me the important question is:
What difference does it make what the we(or an agent) THINK is going to happend tomorrow? This question is motivated by the fact that noone can ever know until its too late!

I would say the difference is that, that a rational agents actions now is guided by it's expectations of the future, it encodes now. Decisions are typically based on incomplete information, so it's essentially a game of expectations. That in a nutshell is my view. And I think essentiall the qbist view as well.
Here one could even argue that wether the expectations are right or wrong, are in fact completely irrelevant. A badly inform agent, will indeed be expected to make "irrational decisions" judged by someone that has different expectations - which should be in principle observable even! This is not a "problem", it's part of the game and learning process.

In qbism the probability is guiding, rather than descriptive. Obviously we can not describe the future, only the past. And there is no deductive inference of the future from the past (or present). And the best inference seem unavoidably relative.

/Fredrik

 

[Fra]

Indeed, but what's the meaning of probabilities for single events? See #156 for further details concerning my question.

I think to elaborate on this in detail. Ie. to "explain" how one can infer a guiding probability from "emprics" without huge amounts of repeats and preparatations, may require a new formalism that unavoidably becomes speculative and involving hypothesis that doesn't belong here.

This is one of the things I expect from a future theory. And while you usually don't associate to it, for me it naturally relates to QG, as the cosmological perspective vs subatomic perspective exactly illustrates the difference between statistics that we can understnad as ensembles, and generalized probability that we can understand without ensembles/prepartion paradigm, and that makes sense even when the ensemble production cant be realized.

/Fredrik

 

[Simple question]

That's a contradiction in it self.

No, that was sound reasoning.
A contradiction is to name "local" a principle like "space-like observable should commute".
The contradiction is in bold.

If there's no FTL "signalling", i.e., no causal connection between space-like separated events in your model,

That's not what FLT "signaling" means. "FLT signaling" means "FLT signaling": communication with no delay.

standard relativistic QFT is indeed not "nonlocal", as we've discussed zillions of times now.

Aside being based on your philosophical misconception of its premises, and AFAIK, standard relativistic QFT did not get rid of entanglement and inseparability. So spatially-extended (non-local) two-particle properties is the bread and butter of QM.

You can interpret any theory in any way you like.

No you cannot. You have to use logic and reason. Unless your prefer bad philosophy and running in circle.

The only restriction is that your interpretation must not contradict the mathematical properties of the model you want to interpret (here it's relativistic QFT).

Mathematical facts don't exist in Nature. Mathematical truth exist in heads. Facts are collected in the laboratory, where your claims of the purported "mathematical facts" have been proved wrong.

 

[DrChinese]

1. These events taken together, i.e. prior to post-selection, constitute the full ensemble.

The photons 1&4 will be uncorrelated in the full ensemble. The statement is true for the post-selected subensembles only.

If you don't look at a subensemble, there will not be entanglement in the data. The correlation will be zero. This follows strictly from the math.

1. No, the full ensemble is maximally entangled. You just don't know how. If you run an experiment, and can identify 1/2 the cases as to Bell state (which is feasible), that portion will violate the CHSH bound. The other half will not show any correlation, as you say. That does not mean they aren't entangled, QM predicts they are.

2. You are being imprecise on purpose here. Quantum non-locality means nothing more than the fact that Bell's inequality is violated.

3. What you want to imply is that there are non-local cause and effect relationships. The broad consensus among physicists is that no non-local cause and effect relationship can be inferred from the data. QM can be interpreted either way.

2. Quantum nonlocality is a lot more than violating a Bell Inequality! The predictions of QM embed the nonlocality. Specifically: cos^2(Alice-Bob) prediction is inherently nonlocal, as Alice and Bob and their measurement settings need not be local to each other. Note that there are no other variables in this equation.

And as we have demonstrated repeatedly in our extended discussions: the particles that Alice and Bob are observing need never have interacted or even overlapped in a common light cone. That's a lot of nonlocality! And how do quantum repeaters work in an extended quantum network? They are built on this nonlocality.3. I never said there was a cause-and-effect relationship in the Einsteinian sense, because there isn't. The action at a distance: a) does not change when the ordering changes (effect precedes cause); and b) and the effect cannot be said to occur at any specific time. You can make a statement about the final context, and say the swap created the entangled 1 & 4 pair. But that is mostly a convenience in describing the situation.

There are other ways to describe it, but since you always have the option to execute a swap or not: this is the most useful. The decision to execute the swap gives you something to point to as the "cause" even though it may be after the "effect". If you feel more comfortable saying the "spontaneous" creation of the (1 & 4) biphoton causes the BSM to succeed, then that is your choice and is just as correct in the final analysis. But again, I would not say this description is useful because the BSM is where the "on/off switch" is located.

 

[PeterDonis]

what's the meaning of probabilities for single events?

Read the Bayesian literature for a detailed answer to this question. The short answer is, it's a measure of a degree of belief. If you want to tie it to something concrete, think of betting odds: a 35% probability of rain tomorrow means that a person would pay 35 cents for a bet that pays 1 dollar if it rains tomorrow.

 

[DrChinese]

This just in! From an experiment described in a paper deposited 15 Jan 2023:

https://arxiv.org/abs/2301.06091

"Photon-pair sources based on spontaneous parametric down-conversion (SPDC) serve as such a resource of entanglement, as they can be matched in frequency and bandwidth to the ionic transitions [4–7]. When entanglement between distant nodes has been established, quantum teleportation [8] provides a suitable protocol, alternative to direct transmission, for quantum state transfer [9]. Application of teleportation has been shown between photons over large distances [10–15], between quantum nodes [16–20], and from a photon to a quantum node [21–24]. In this paper we show quantum teleportation of an atomic qubit, encoded in the Zeeman sub-levels of the 40Ca+ ion, to the polarisation qubit of a single 854 nm photon. The teleportation protocol employs heralded absorption of a single photon by the ion [4, 9, 25, 26], which functions as a Bell measurement. In contrast to photonic teleportation protocols, this Bell measurement can identify all four Bell states."

All 4! Where's the subensemble "out" now?

They ran 500 million swaps (teleportations) over a 50 hour period. They identified all 4 Bell states with approximately 81% fidelity.

Pure optical setups may be limited to discerning a maximum of 2 Bell state due to limitations inherent in Avalanche Photon Detectors (APD). That's because a single APD cannot distinguish 2 photons that arrive in close proximity from a single photon, which would be necessary to identify 2 of the 4 Bell states. They can't reset fast enough - at least not at this time.

But technology advances, and red herrings fall. There is nothing about the BSM (pre- or post-) selection process that is can be considered "cherry picking".

As I was saying in the entanglement swapping scenarios: All of the cases (in principle) where we have (1 & 4) matched clicks indicate entanglement swapping. This can be seen in this experiment, although it is expressed differently than in the swaps we have been discussing. Hopefully everyone can see clearly: there are no (1 & 2) pairs where there is "coincidental" or "accidental" entanglement between 1 & 4 waiting to be revealed. If there is no swap (teleportation), there is no entanglement to be seen. If and only if...

 

[akvadrako]

All 4! Where's the subensemble "out" now?

There are 4 subensembles. You still need to know which runs belongs to which to get entanglement.

This doesn't change anything about the discussion; as several people have pointed out, it would have been clearer to just consider the ideal experiment, where there is no need for an event ready signal.

 

[DrChinese]

1. There are 4 subensembles. You still need to know which runs belongs to which to get entanglement.

2. This doesn't change anything about the discussion; as several people have pointed out, it would have been clearer to just consider the ideal experiment, where there is no need for an event ready signal.

1. And they did. Case closed.

2. The original post-selection "out" was that only *some* of the pairs were being considered. Most of the optical versions could only identify 1 or 2 of the Bell states, and some folks saw that as explaining that only the "cherry-picked" sample would show entanglement - but the full data set would not.

Obviously: If you can identify the entanglement of the full universe, then the cherry-picking argument fails. It never made sense anyway, as *all* of the 1 & 4 pairs are entangled according to the predictions of QM (perfect case of course). So unless you have alternate and different predictions to make, I don't see the point of that line of reasoning.

I hope the debate about "subensembles" will shift to something more appropriate. Like the obviously nonlocal nature of entanglement swapping in which a CHSH inequality is violated by systems that have never been in a common light cone (and need not have ever even communicated with systems in a common light cone).

 

[mattt]

For each of the four (1,4) subensembles, (1,4) will violate a Bell inequality (after all, for each of those (1,4) subensembles, the state that describes its statistics is, respectively, a maximally entangled state).

But for the four subensembles taken together, its state (which describes its statistics) tells you that it will not violate a Bell inequality (the whole (1,4) ensemble).

 

[Morbert]

1. No, the full ensemble is maximally entangled. You just don't know how. If you run an experiment, and can identify 1/2 the cases as to Bell state (which is feasible), that portion will violate the CHSH bound. The other half will not show any correlation, as you say. That does not mean they aren't entangled, QM predicts they are.

This distinction you are implying (unentangled pairs as distinct from hidden entangled pairs) isn't inherent in the formalism. It's also a double-edged sword. The consistent histories interpretation lets us split the full ensemble into subensembles of entangled (14) pairs even if the BSM on (23) is never performed.

 

[akvadrako]

2. The original post-selection "out" was that only *some* of the pairs were being considered. Most of the optical versions could only identify 1 or 2 of the Bell states, and some folks saw that as explaining that only the "cherry-picked" sample would show entanglement - but the full data set would not.

You are missing the point. It was always an aspect of the idealized experiment that you select 4 sub-ensembles, each entangled. And nobody was arguing that it was only the non-ideal experiment that allowed an "out" due to low fidelity.

One still needs to "cherry-pick" those 4 sub-ensembles to show entanglement. If you perform the entanglement swapping but then throw away the information of which runs are in which sub-ensemble, you will never be able to show any entanglement.

Which I would say is the same as saying there is no entanglement, because entanglement is not an objective property of pairs of systems, but a statistical correlation. It's some subjective information. The monogomy of entanglement means you can never have information like pairs A&B are fully entangled while B&C are fully entangled.

 

[DrChinese]

For each of the four (1,4) subensembles, (1,4) will violate a Bell inequality (after all, for each of those (1,4) subensembles, the state that describes its statistics is, respectively, a maximally entangled state).

But for the four subensembles taken together, its state (which describes its statistics) tells you that it will not violate a Bell inequality (the whole (1,4) ensemble).

This is one of the strangest comments I have ever seen, completely meaningless and essentially contradictory.

We're scientists. You may as well be saying the results from looking at only the 1 stream are random. True, but of no value whatsoever. I guess that means Bell tests are evidence of nothing.

 

[DrChinese]

This distinction you are implying (unentangled pairs as distinct from hidden entangled pairs) isn't inherent in the formalism. It's also a double-edged sword. The consistent histories interpretation lets us split the full ensemble into subensembles of entangled (14) pairs even if the BSM on (23) is never performed.

When the BSM is turned on, all of the 1 & 4 pairs are entangled. When the BSM is not performed, none of the 1 & 4 pairs are entangled. How many ways can I say the same thing?

 

[PeterDonis]

The consistent histories interpretation lets us split the full ensemble into subensembles of entangled (14) pairs even if the BSM on (23) is never performed.

Please give a reference for this very surprising statement.

 

[PeterDonis]

One still needs to "cherry-pick" those 4 sub-ensembles to show entanglement.

No, you don't. The subensembles for photons 1 & 4 are defined by the results of the BSM on photons 2 & 3. "Cherry picking" would be using the results on photons 1 & 4 to pick "subensembles" for photons 1 & 4.

 

[DrChinese]

One still needs to "cherry-pick" those 4 sub-ensembles to show entanglement. If you perform the entanglement swapping but then throw away the information of which runs are in which sub-ensemble, you will never be able to show any entanglement.

Which I would say is the same as saying there is no entanglement, because entanglement is not an objective property of pairs of systems, but a statistical correlation. It's some subjective information. The monogomy of entanglement means you can never have information like pairs A&B are fully entangled while B&C are fully entangled.

Again, a strange comment.

In science, we look for patterns and pattern exceptions. Yes, if you throw half of your experimental data away, then probably you won't see much of a pattern. Who does that? And why would any scientist suggest that?

This is state of the art experimentation, and if you choose to ignore the evidence of entanglement: I really have nothing more to discuss with you. Not sure why you would participate if you think looking at ALL of the data is "cherry-picking". And why would you say there is NO entanglement when all 4 Bell states shows entanglement?