lodbrok said:
Heralding in the context of these experiments means to signal that an event meets a particular criterion. It is a filtration or selection flag. The following analogy is appropriate:
For each iteration (#i), you send randomly coloured pairs of socks [1&2] and [3&4] to two different remote locations. Midway through the trip, the pairs are separated so one member of each pair (1 and 4) goes to station A, and the other (2, 3) goes to station B. At station B, a BSM experiment is performed, which in this analogy is equivalent to asking the question "are both socks the same colour?". If the answer is "Yes", the supervisor writes down the number (#i) in his journal (aka "Supervisor's Herald"). If the answer is "No", he ignores it and continues evaluating pairs of socks [2&3] as they come in for many thousands of iterations.
Back at station A, another supervisor has been evaluating incoming pairs [1&4] of socks independently also and keeping the results in a table where she writes down the numbers (#i) next to her results "Yes" or "No". Based on the distances from the socks factory to stations A and B, these "measurements" may happen at different times with A happening before B or vice versa.
The day after the experiments, the supervisors both travel to a third location, taking just their journals with them. Supervisor B notes that the entries in her table are completely random switches between "Yes" and "No". Supervisor A says, "let us filter your spreadsheet and use just the rows with just the numbers from my Herald!". After doing that, they find that all those rows are always "Yes".
Does this mean anything was transferred from any particular pair of socks to any other pair of socks? No! It simply means you are using the information from the [2&3] interaction to post-select a subset from the [1&4] interaction data that would show a correlation, despite the fact that the full [1&4] data does not show any such correlation. ...
All: Please read this entire post, as I have attempted to construct a clear explanation of why entanglement swapping experiments are in fact a proof that local causality in untenable. All of my explanation follows standard QM and actual experiment.
@lodbrok: I can't believe you consider this analogous to entanglement swapping. Nothing about your example is suitable.
First: Bell inequalities are violated in your [1 & 4] sample because the quantum world is contextual. Certainly you know about Bell's story about Bertlmann's socks, else why mention socks? Socks don't cut it, we already know this. You cannot hand devise a data set that matches quantum predictions without knowing what is to be measured (I get to decide, not you, otherwise cheating is possible). Gotta handle perfect correlations AND other angles. That cannot be done - i.e. your example failed this test.
Second: In actual swapping experiments: the [2 & 3] selection process does not allow for enough information to be collected to determine that the [1 & 4] pairs will be like entangled as you imagine. The actual information the guy in the middle gets:
a) The pair arrives at the same time for examination, meeting the coincidence window requirement.
b) The pair both pass identical filters at a specified wavelength.
c) The pair has known and opposite polarization, having passed through a filter. Some swapping experiments such as one from the
Gisin team use a polarizing beam splitter after the d) step, but others such as the
Hanson team use polarizers place before the d) step. Note that this step is performed in order to cast/select the psi- Bell state, which requires that the [2] and [3] photons are either HV or VH. Note that the specific orientation of the polarizers is not relevant, just that they are 90 degrees apart. For our example, we will assume the polarizers are are placed as in the Hanson team's, with an H polarizer on one and a V polarizer on the other. Although they don't identify which is which, we will make the assumption that the [2] photon gets a H polarizer, and the [3] photon gets the V polarizer.
d) The pair consists of either both transmitting through a beam splitter, or both reflecting at the same beam splitter.
e) No action here, just a placeholder for later.
Obviously, the first 5 steps a) to e) have a classical analog and will in fact produce a sample. In the Hanson team paper, there were 245 successful swaps. So I grant you: these 5 steps would be fine in your socks example on the Bell State Measurement side - so far.
f) The [2] & [3] pairs are detected in their source indistinguishable state, and are heralded by 2 fold coincidence on the 2 detectors (let's call them L and R). You don't know if the L photon detector measures the [2] photon or the [3] photon (and vice versa). You don't know which photon is [2] and which is [3], because you don't know whether they were both reflected or both transmitted. There is no classical analog to this, and it is a requirement for a successful swap. You can't mix up classical socks to perform this experiment. So your analogy fails again.
Third: There are several interesting issues here. Step d) involves having the [2] and [3] photons to overlap in a small physical region of a 50:50 beam splitter. Perhaps they interact in some fashion? No, that is NOT possible: one is H> and the other is V>. By definition, they are fully orthogonal and therefore cannot interact or interfere or otherwise be changed in any manner. However, this step d) does select a subsample from the inputs. Cases in which the [2] photon is reflected and the [3] photon is transmitted (and vice versa) are excluded - because only one of the two detectors (either L XOR R) will click. To get the entangled Psi- case, we need both detectors to click. Yet we do get a subset/sample that "selects" 245 successful swaps that indicate the [1 & 4] pairs will have perfect (anti)correlations and violate a Bell inequality such as CHSH. These will consist of 2 groups that reach the L and R detectors, totaling 245* in the cited experiment:
i) L detector clicks on receipt of the [2] photon (H polarized), R detector clicks on receipt of the [3] photon (V polarized). Let's pretend there are 127* in this group, although we don't actually know.
ii) L detector clicks on receipt of the [3] photon (V polarized), R detector clicks on receipt of the [2] photon (H polarized). Let's pretend there are 118* in this group, although again we don't actually know.
These scenarios should occur with random and near equal frequency, and cause/select/herald/cast a successful swap for [1 & 4] pair. According to the "post-selection" school of thought, there is no further action at the BSM (where the [2 & 3] sample is identified) that could CAUSE the [1 & 4] groups to stop being correlated. How could they, the argument goes, since we have selected our correlated sample of [1 & 4] pairs? They are too distant to CAUSE a change at this point!
Well guess what... and this is the cool part! Suppose we could magically take our sample consisting of cases i) and ii) - all of which herald successful swaps - and identify just group i) experimentally? If you did that, you would no longer meet the source indistinguishability requirement - and the heralded [1 & 4] pairs would no longer be entangled. How, you ask can this be accomplished?
Go back to our step e) above - the one where nothing happens between the Beam Splitter and the L and R detectors. Instead of doing nothing, let's add an H polarizer in front of the L detector, and an V polarizer in front of the R detector. Voila, we can now distinguish case i) : as only the [2] photons can pass the H polarizer in front of the L detector (which will still click), only the [3] photons can pass the V polarizer in front of the R detector (which will also click). This time, QM predicts the 127 [1 & 4] pairs will not demonstrate any particular correlations.**
Our decision to do nothing - or something - for step e) above CAUSES - without any ambiguity whatsoever - the statistics of the DISTANT [1 & 4] pairs to change (from Entangled State statistics to Product State statistics). That is because the entanglement swapping operation is a physical process/event/action that is essential to the outcome. It cannot be considered as a mere "selection" of a subset, as we select the exact same swap events but get different results.
Please note this important caveat: I have intentionally capitalized the word "CAUSE" in order to distinguish it as being a CAUSE in the quantum mechanical sense. Note that this CAUSE (a successful Bell State Measurement/BSM, or not) can occur *before*, *after*, or *during* the EFFECT - which is the observed statistics of the [1 & 4] pairs (i.e. the Bell test is the effect). And importantly, all this happens regardless of DISTANCE (outside of light cones) from the BSM (cause) to the Bell test (effect). Classical causality would require a cause to occur *before* the effect, and within a distance bound by c. So the kind of causality I assert occurs in the quantum world does not meet any kind of classical definition, which matches precisely the predictions of QM.
There is no local causality, and any theory or interpretation that claims otherwise is invalidated by entanglement swapping experiments.
-DrC
PS If you spot an error in the above, please let me know. These experiments are notorious difficult to follow.*Obviously, a rerun of this experiment would generate different numbers than the 245 (= 127 + 118). But they would be similar. In the actual experiment: "
We run 245 trials of the Bell test during a total measurement time of 220 hours. Figure 4a summarizes the observed data, from which we find S = 2.42 in violation of the CHSH-Bell inequality S ≤ 2."
** Please note that I have not seen this particular variation performed in a published experiment, but it is a direct prediction of standard QM. Obviously, it is always a requirement of a successful swap that the [2] and [3] photons be indistinguishable: "
If the [2 & 3] photons are indistinguishable in all degrees of freedom, the observation of one early and one late photon in different output ports projects the spins at A [1] and B [4] into the maximally entangled state |ψ> − = (|↑↓> − |↓↑>) / √ 2 ..."
2. Of course Victor's future action changes the past. That's the entire point, my friend! Quantum mechanics does NOT respect Einsteinian causality, even in direction of causality. Victor's action to entangle the distant pair can be done anytime and anywhere, as experiments actually demonstrate. It could be in the past, present or future. It could be near or distant. Is this paradoxical? Yes! Is it consistent with QM? Yes! To reference the late great Asher Peres (see