# Does QFT prevent preparation of an entangled particle pair as in EPR experiment?

This is the claim Tommasini makes in Reality, Measurement and Locality in Quantum Field Theory:"Two spin $1/2$ particles, A and B, are created in coincidence in a spin-singlet state, and are detected by the detectors $O_A$ and $O_B$ in opposite directions... The EPR argument, as described above, and (as far as I know) all the subsequent treatments of the EPR paradox, have assumed that it was actually possible to prepare a system of two entangled particles. However, I have recently proved that this assumption is not correct... In fact, the Standard Model of Particle Physics predicts that it is not possible to produce a state having a definite particle content: given the process that produces A and B alone, QFT theory predicts a nonvanishing and finite probability for the creation of A and B plus additional photons".

She goes on to say that "the EPR+Bell proof of nonlocality is removed" because "for the EPR argument it is crucial that the measurement on A implies a certain prediction for B without disturbing B". But spurious photons potentially produced along with A and B make any prediction uncertain.

Is it true that in QFT one can not prepare states with prescribed number of particles? Does it follow that above analysis of EPR is correct? QFT is manifestly relativistic, so it makes sense that quantum non-locality is "removed", and Tommasini reproduces the usual QM correlations for EPR using a Feynman integral QFT calculation, so it seems consistent. But this diverges sharply from the usual explanation of EPR.

EDIT: In a companion paper there are some details on computations and agreement with experiments:"the case of the EPR experiments that have been performed up to now the QED prediction for the correlations is very close to that obtained in Quantum Mechanics by ignoring the soft photons, so that it can still agree with the data within the experimental errors. However, even a very small probability for soft photons creation is sufficient to forbid any certain prediction for the measurement on B as a consequence of the measurement on A".

Apparently, soft photons do exist (her source is Weinberg's text), and they do affect QED predictions:"Even though soft photons are not detected, the possibility of their emission must be taken into account in the calculation of the scattering amplitude". Entanglement and the infrared structure of QED discusses QED violations of Bell inequalities:"We might consider that they started with the studies of the effect of the QED spin-spin interactions on the entanglement and the violation of Bell Inequalities due to QED... The objective of this work is... to characterize the effect of soft photons on the entanglement of two charged qubits..."

So I guess the answer to the first question is affirmative. I am still not clear though why small QED corrections to QM correlations entirely "remove" non-locality.

• I think those experimentalists who actually have prepared EPR pairs of photons or qubits in lab (many, many times) and measured them would happily disagree with whatever that paper said. – Meng Cheng Jul 17 '15 at 2:24
• @Meng Cheng I think her point is not that a pair can not be produced, but that one can not produce only the pair with certainty. Weinberg discusses soft photons, they are confirmed in particle collisions and they do introduce QED corrections to QM correlations, but too small to be detected in Aspect type experiments. She might be overstating her case though: even though QED corrections are enough to make the spin measurement of B slightly uncertain and dissolve EPR "element of reality" argument, I am not sure that "removes" non-locality like she says. I added some context on experiments. – Conifold Jul 19 '15 at 3:58

As is often the case with these sorts of papers, it is sometimes difficult for me to tell if the author is making a trivial statement, or a sophisticated one that I don't understand. So any other viewpoints on the content are welcome. With that disclaimer, here is my understanding:

The author appears to put an extreme emphasis on the following words in the original EPR paper:

If, without in any way disturbing a system we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there is an element of physical reality corresponding to this physical quantity

Then he (the author is male) goes on to point out something that I can't independently confirm but seems reasonable: one cannot make a perfect preparation of the original two-particle entangled state in QED. There will always be some admixture of other states. So you will never truly predict the outcome of this (or any other!) experiment with unity, and therefore the prerequisite for EPR as stated above is never satisfied. Of course, our uncertainty may get arbitrarily low, but perhaps any uncertainty in principle is enough to ruin this "element of physical reality."

Okay, but how important is this? From my perspective, the answer is "not very," for the following reason:

From my viewpoint, the original EPR paper, while hugely important, is really only of historical significance now. The most important thing it did was to partly inspire Bell's work. Now, the violation of Bell inequalities, and the resulting implications for hidden variable theories of quantum mechanics, do not require any such perfect preparation and as a result are completely unaffected by this issue. Tommasini says this himself. Since this is what our understanding of quantum mechanics is based on, I don't see any reason that this claim should change anything about how we think about the nature of QM.

It is usually thought that the violation of Bell's inequality was a unambiguous refutation of the claims made in the EPR paper. Tommasini says this is not true, and that because of this imperfect preparation both papers are addressing slightly different situations. This is a historical question that might interest some people. But, from my perspective, what Bell experiments say about an 80-year-old paper that may or may not be asking a completely well-posed question is less interesting than what they say quite unambiguously about nature itself.

Finally, the author worries that we might be missing something about the viability of quantum teleportation or quantum computing because of this issue. Quantum teleportation had already been first achieved some years before this was published, and has continued to be used in more and more elaborate ways. Quantum computing is also growing in sophistication, without any disagreement with theories that neglect soft photon emission as far as I know. So, while maybe valid when this paper was written, I would say this worry is basically unfounded by now.

• Thanks, one other thing I don't understand, does QED shed any new light on "collapse"? She is saying that there can be even no apparent collapse because QED is relativistic, and so EPR experiment has to be reinterpreted in terms of ensembles, or something like that, which restores locality. Is QM interpretation of EPR altered by QED in some such way? – Conifold Jul 20 '15 at 23:31
• I think many-to-most physicists would agree that wavefunction collapse should be regarded as a convenient proxy for using QM, but not a true physical process. Solutions to the measurement problem that have an explicit collapse (like GRW) are not very popular, and Tommasini gets at some of the reasons why. However, I would say that he overstates the case for his favorite solution being the most reasonable way to solve this. For many, many more opinions on this you can look around at arguments for various QM interpretations on this site and elsewhere. – Rococo Jul 21 '15 at 0:06
• I did, but for all the QM interpretations out there I found very few sources on interpreting QFT, Tommasini being one of them. For example, I do not see how something like QM collapse can be expressed in QFT at all, even as a non-physical process, I even asked about it, but nobody answered physics.stackexchange.com/questions/193918/… – Conifold Jul 21 '15 at 1:22
• Yes, this is something that I don't know very much about either. I suspect that Tommasini is in the minority in claiming that the difference between relativistic QFTs and non-relativistic QM is relevant to interpretations. – Rococo Jul 21 '15 at 2:05