How do you determine that a particle is/was entangled?

[Cthugha]

I don’t care how you spin what Zeilinger said – it comes down to agree with just what Dr C says in post #27.
I understand he is an important guy, but proof by authority does not work for me but I had not been able to find a documented experiment that demonstrates the point.

I disagree. One of the important restrictions Zeilinger mentions in his paper is that the interference pattern will vanish for perfect correlations between both photons. However this perfect correlation is only possible in a near-field setup. Going to far-field conditions automatically destroys your entanglement (see below), so I think Zeilinger is well aware of using a near field setup. So let me paraphrase the wording of Zeilinger again: There is no possible setup, in which you can maintain entanglement and go to far-field conditions simultaneously.

It focus on the pattern observed in Fig 2.
Unless you can explain how any a)more, b)less or c)different photons will show at the Ds detector by not limiting the count there with Dp correlations (IE turn Dp off & count all Ds hits) how can it not show the same interference pattern.

You will see more photons. In coincidence count experiments there are in fact two interference patterns. One is shown here, which is the result of moving the Ds detector. The detector Dp is stationary and small. You will see another interference pattern if you leave Ds stationary and instead move Dp and this interference pattern will be exactly out of phase with the other one. This has been shown in the Dopfer thesis and also in the Kim DCQE paper if I remember correctly. So by detecting all photons, which is equal to increasing the size of Dp you will see the superposition of both patterns, which is a simple peak without interferences.

It seems to me you can take separated entangled photons and then aim them at a double slit while preserving their momentum entanglement. You should be able to aim them with sufficient precision (and the appropriate angular size) to get an interference pattern - if there is one to get. I don't think an interference pattern will form in such circumstances, and I think that is the point that Zeilinger is making.

I don't think so. The range of possible k-values and therefore also momentum values narrows strongly if you increase the distance between double slit and the SPDC crystal. At some point you just have a momentum filter and the concept of entanglement is not meaningful anymore. As soon as you reach this distance the entanglement vanishes and at this point the single photon interference pattern starts to show up.

Another light source might however show an interference pattern at the same distance from the slit. This is a question of spatial coherence.

 

[JesseM]

Reread the experimental results in your first link with attention to:

- The first two lines of sect V.
- Also, the comments between formulas 6 & 7 to confirm that this actually preformed experiment was conducted in a “Far Field” set up. (A requirement to produce the interference pattern with or without the beam on the double slit originating from a entanglement source.)
- The results in Figure 2
They contradict the Zeilinger claim as we have discussed before in prior threads.

No they don't, because Fig. 2 clearly shows they are dealing with interference in the coincidence count, not the total pattern of photons.

Since no filters are in place anywhere in the Fig 2 test; 100% of the S photons are used.
Even if the correlation counter turned off the same 100% of the S photons would be detected in the same place just as shown in Fig 2.
Remember Dp I positioned to collect all photons unless blocked by a polar filter; no lens or slits scatter any of them away from Dp. Ds must be moved due to the slit scattering.

Nowhere do they say "Dp is positioned to collect all photons", this is just your own unjustified notion. In fact if you look at the diagram of the setup on http://grad.physics.sunysb.edu/~amarch/ you can see a double-headed arrow next to the bottom detector Ds, indicating that the detector itself has a very narrow range and that they have to actually move it back and forth over many trials in order to build up the coincidence count seen in fig. 2:

http://grad.physics.sunysb.edu/~amarch/PHY5655.gif

The text on that page also says explicitly that Ds has to be moved around by tiny increments to build up the graph in fig. 2, also clearly showing that at any given position Ds cannot detect the full range of positions seen on the horizontal axis of fig. 2:

The counts are tallied for 400 seconds. Then detector Ds is moved a millimeter and the number of counts in a 400 second interval is recorded for the new detector position. This is repeated until Ds has scanned across a region equivalent to the screen in the diagrams above.

Presumably the top detector Dp has an equally narrow range, and thus at any fixed position, there will be a lot of p-photons that miss it because they go slightly to the left or the right (it's not just scattering off the slits that causes photons to fail to go in a straight line as you seem to suggest in last sentence of the paragraph I quoted, there's also the position/momentum uncertainty relation--since we know the approximate position the p-photons were emitted from at the BBO crystal in the diagram, there has to be some spread in the directions they travel). As I said on the Double slit experiment thread, I'm pretty confident you could put an array of different Dp detectors side by side and get some p-photons going to each one:

Note that even with the quarter-wave plates absent (the first diagram in the 'Experimental Investigation' section of the page), they only graph cases where an s-photon was registered at Ds and the entangled p-photon was registered at Dp, there might be plenty of cases where an s-photon was registered at Ds but they didn't graph it because the entangled p-photon missed the narrow range covered by Dp. If you put an array of photon detectors at different positions alongside Dp and called them Dp-1, Dp-2, Dp-3, etc., so that close to 100% of the p-photons would be detected by one of the Dp-detectors, then some s-photons at Ds would have their entangled p-photons register at Dp-1, some would have their entangled p-photons register at Dp-2, and so forth. Then the Ds/Dp-1 coincidence count would show interference, as would the Ds/Dp-2 coincidence count and so forth, but if you added all these separate coincidence counts together I believe you'd get a non-interference pattern.

 

[RandallB]

I disagree. One of the important restrictions Zeilinger mentions in his paper is that the interference pattern will vanish for perfect correlations between both photons. However this perfect correlation is only possible in a near-field setup. Going to far-field conditions automatically destroys your entanglement (see below), so I think Zeilinger is well aware of using a near field setup. So let me paraphrase the wording of Zeilinger again: There is no possible setup, in which you can maintain entanglement and go to far-field conditions simultaneously.

But obviously this experiment IS set up in the “Far Field” and I have no doubt that any Bell Test here and ASFIK all Bell tests are at a Far Field distance. To prove me wrong your just going to have to do a Bell Test to confirm a entangled beam remove one of the Bell detectors (and ignore the other beam) insert a double slit known to work with a plain beam set at a similar distance as from the PDC as see if you get the pattern or not.

You will see more photons. In coincidence count experiments there are in fact two interference patterns. One is shown here, which is the result of moving the Ds detector. The detector Dp is stationary and small. You will see another interference pattern if you leave Ds stationary and instead move Dp and this interference pattern will be exactly out of phase with the other one. This has been shown in the Dopfer thesis and also in the Kim DCQE paper if I remember correctly. So by detecting all photons, which is equal to increasing the size of Dp you will see the superposition of both patterns, which is a simple peak without interferences.

Did you read the same experiment, or just skim through it?
Dp is not set the same as in Dopher near field set up.
This is a far field configuration and Dp is clearly set closer to collect as closely as possible 100% of the Photons (that correlate with photons) that arrive at the FRONT of the double slit. (there are no test design limits on the size of Dp while obviously Ds must be designed small enough to detail a pattern – just as obvious the design of the test would ideally collect all possible photons at Dp that correlate with any photon that might hit the slits area – “well yah duh” )
The only thing that limits the count here is the photons Blocked by the double slit. If you move Dp you will not get any correlations! Where are these “more photons” you claim to come from?

To maintain what your believe, the three of you are ad hoc revising the documented results of the experiment DrC found; Presuming to presume whatever you chose to be Presumably correct.
I’ll stick with the unabridged direct results of experiment as reported as my reference.
And I am more than satisfied that contrary to Zeilinger, testing two otherwise identical beams (one coming from half the output of a PDC) with a double slit will not be able to indentify which one came from the entangled source.

PF does not need another endless thread, so I will stand aside and allow one of you the BE the “thread ender”.
It will give you another thread “authority” to quote as a reference, but it won’t mean your right.

 

[DrChinese]

No they don't, because Fig. 2 clearly shows they are dealing with interference in the coincidence count, not the total pattern of photons.

Nowhere do they say "Dp is positioned to collect all photons", this is just your own unjustified notion. In fact if you look at the diagram of the setup on http://grad.physics.sunysb.edu/~amarch/ you can see a double-headed arrow next to the bottom detector Ds, indicating that the detector itself has a very narrow range and that they have to actually move it back and forth over many trials in order to build up the coincidence count seen in fig. 2:

http://grad.physics.sunysb.edu/~amarch/PHY5655.gif

...

Nice reference! I think the web page summarizes the content of the published article very nicely.

 

[Cthugha]

But obviously this experiment IS set up in the “Far Field” and I have no doubt that any Bell Test here and ASFIK all Bell tests are at a Far Field distance.[...]
Did you read the same experiment, or just skim through it?
Dp is not set the same as in Dopher near field set up.
This is a far field configuration and Dp is clearly set closer to collect as closely as possible 100% of the Photons that arrive at the FRONT of the double slit. The only thing that limits the count here is the photons Blocked by the double slit. If you move Dp you will not get any correlations! Where are these “more photons” you claim to come from?

Three things: The collection slits alone are 300 micrometers times 5 mm large. I don't think this is large enough to collect all photons. Dp does not collect any photons from the front of the double slit (it is in the other leg of the experiment). And yes, I commented on a more Dopfer-like setup. I thought, we were discussing Zeilinger's statement here and Zeilinger talks about momentum entanglement, not about additional polarization entanglement. All my posts in this topic so far were about momentum only entanglement.

In the far field setup used in the Walborn paper the momentum entanglement becomes meaningless, but the polarization entanglement is of course intact. However this is not, what Zeilinger was talking about initially. Considering polarization entanglement is a bit more difficult, but the principle stays the same. This has also been published. See for example page 3601 of the paper "observation of two-photon "ghost" interference and diffraction by Strekalov, Sergienko, Klyshko and Shih (PRL 74, 18, 1995 free version here:http://puhep1.princeton.edu/~mcdonald/examples/QM/strekalov_prl_74_3600_95.pdf ).

There it is explicitly stated that "Even though the interference-diffraction pattern is observed in coincidences, the single detector counting rates are both observed to be constant when scanning detector D1 or D2". The distances of roughly 1m used here are certainly far field as well.

 

[Hans de Vries]

http://grad.physics.sunysb.edu/~amarch/PHY5655.gif

http://grad.physics.sunysb.edu/~amarch/
http://grad.physics.sunysb.edu/~amarch/Walborn.pdf

Nice, experiment.

Note however that all results are just what one would expect from classical optics...


If you look at the pdf.

FIG 2: The interference pattern.

FIG 3: The interference pattern disappears after the insertion of the quarter-wave plates.

The pattern also disappears in classical optics: The Left plus Right hand polarized light
produces TWO interference patterns. One for horizontal and one for vertical polarized light.
The two patterns are 180 degrees displaced relative to each other and together they
sum up to the "non-interference" pattern of Figure 3.


FIG 4: The interference pattern reappears if a 45 degrees polarizer is inserted in the other beam.

This is actually one of the two interference patterns mentioned above. The polarizer
absorbes ~70% of the photons and 45 degrees polarized photons have the highest
change of getting through.

Therefor the -45 degrees photons at the dual split side have the highest change of
getting counted. What does happen now at the quarter-wave plates? Look at the table
in the middle of http://grad.physics.sunysb.edu/~amarch/

QWP1:  0 degrees --> Right polarized light, 90 degrees --> Left  polarized light
QWP2: 90 degrees --> Left  polarized light,  0 degrees --> Right polarized light

Under 45 (or -45) degrees they both produce linear polarized light. Either both horizontal
or both vertical light. Figure 4 therefore corresponds with one of the two interference
patterns adding up to the "non-interference" pattern of Figure 3.


FIG 5: A 180 degrees displaced pattern appears if photons which tend to have a -45 degrees polarization are counted.

This is the other of the two interference patterns adding up to Figure 3. The displacement
of the interference pattern is determined by classical optics. Figures 4 and 5 add up to
Figure 3 as they should do.




Regards, Hans

 

[JesseM]

http://grad.physics.sunysb.edu/~amarch/
http://grad.physics.sunysb.edu/~amarch/Walborn.pdf

Nice, experiment.

Note however that all results are just what one would expect from classical optics...


If you look at the pdf.

FIG 2: The interference pattern.

But that with no quarter-wave plates, the interference pattern is only visible in the coincidence count of detections at both Ds and Dp as shown in Fig. 2, if you looked at the total pattern of photons at Ds without doing any coincidence-counting you wouldn't see an interference pattern in this case (no non-coincidence graphs are actually shown on that webpage, but this follows from what we'd been discussing earlier on the thread)...would that also be true in classical optics?

 

[Hans de Vries]

But that with no quarter-wave plates, the interference pattern is only visible in the coincidence count of detections at both Ds and Dp as shown in Fig. 2, if you looked at the total pattern of photons at Ds without doing any coincidence-counting you wouldn't see an interference pattern in this case (no non-coincidence graphs are actually shown on that webpage, but this follows from what we'd been discussing earlier on the thread)...would that also be true in classical optics?

Well there are no photons of course in classical optics, but you would get the two interference
patterns of Figure 4 and Figure 5 if you shine either 45 or -45 degrees linear polarized light on the
double split setup including the quarter wave plates, and no interference pattern if the light was
randomly linear polarized.

Regards, Hans

 

[Hans de Vries]

Well there are no photons of course in classical optics, but you would get the two interference
patterns of Figure 4 and Figure 5 if you shine either 45 or -45 degrees linear polarized light on the
double split setup including the quarter wave plates, and no interference pattern if the light was
randomly linear polarized.

Regards, Hans

It seems from the pdf that the quarter wave plates are simply the ones described here.

http://en.wikipedia.org/wiki/Wave_plate

A simple birefringent crystal where H and V polarized light travels at different speeds
and exit the cristal with a 90 degrees relative phase shift between the two. This turns
the linear polarized light in circular polarized light depending on the angle.

If the linear polarized light is aligned with either the fast axis or the slow axis then
it will stay linear polarized light.

From to the pdf:

Introducing the λ/4 plates one in front of each slit with the fast axes at angles θ1
= 45° and θ2 =-45° to the x direction

This means that, according to classical optics, linear polarized light at 45° or -45° will stay
linear polarized light a 45° or -45° and interference should occur.

In this particular experiment I don't see any deviation from classical optics, unlike the
Wollaston prism experiments where Malus law doesn't predict the outcome for individual
entangled photons.Regards, Hans.

 

[JesseM]

In this particular experiment I don't see any deviation from classical optics, unlike the
Wollaston prism experiments where Malus law doesn't predict the outcome for individual
entangled photons.

But this experiment is all about coincidence counts between photons at one detector and entangled photons at another--it's only in the coincidence counts that the interference effects are seen, the total pattern of light at the Ds detector wouldn't show interference in any phase of the experiment. Since there's no analogue for coincidence-counting of entangled particles in classical optics, and you say that in classical optics the total pattern of light at the position of Ds would show an interference pattern in the setup with the quarter-wave plates, it seems strange to say "I don't see any deviation from classical optics".

 

[Hans de Vries]

But this experiment is all about coincidence counts between photons at one detector and entangled photons at another--it's only in the coincidence counts that the interference effects are seen, the total pattern of light at the Ds detector wouldn't show interference in any phase of the experiment. Since there's no analogue for coincidence-counting of entangled particles in classical optics, and you say that in classical optics the total pattern of light at the position of Ds would show an interference pattern in the setup with the quarter-wave plates, it seems strange to say "I don't see any deviation from classical optics".

There's a very distinct difference between the usual EPR experiments with a Wollaston prism
and this experiment:

The angle of linear polarization of the photons explains all the results.

This angle is what is used as the "Bohm hidden variable" in other EPR experiments where it
fails to explain the experimental results.


Regards, Hans

 

[DrChinese]

Well there are no photons of course in classical optics, but you would get the two interference patterns of Figure 4 and Figure 5 if you shine either 45 or -45 degrees linear polarized light on the double split setup including the quarter wave plates, and no interference pattern if the light was randomly linear polarized.

This cannot be accurate, because classical optics does not provide a theory of entangled waves either. That is what we would need to model - where is that model? Is there a reference?

And yet, ordinary EPR experiments rule all such models out a priori! So trying to model a classical explanation of a Quantum Eraser experiment fails before we get started. On the other hand, all QM-based models must be able to explain/predict the results of these experiments... and they do.

So I completely disagree with any statement to the effect that a classical model can explain the series of results in the reference supplied above by JesseM.

 

[Hans de Vries]

So I completely disagree with any statement to the effect that a classical model can explain the series of results in the reference supplied above by JesseM.

Well that's very outspoken. Let's study the experiment then and go through it step by step:

Classical optics tells us that:

1) +45° linear polarized light will produce an interference pattern.
2) -45° linear polarized light will produce an interference pattern displaced by 180°
3) A mix of arbitrary linear polarized light will produce no interference pattern

Why do you think this is wrong from a classical optics point of view?

Regards, Hans

 

[Hans de Vries]

1) +45° linear polarized light will produce an interference pattern.
2) -45° linear polarized light will produce an interference pattern displaced by 180°
3) A mix of arbitrary linear polarized light will produce no interference pattern

+45° polarized light is on the fast axis of one birefringent quarter-wave plate and on
the slow axis of the other quarter-wave plate. It sees only a single refraction index per
quarter wave plate. The lower one on the first and the higher one at the second.

The photon stays +45° linear polarized at both quarter-wave plates and an interference
pattern occurs. The only difference due to the quarter wave plates are the absolute and
relative phase shifts, introduced by the propagation through the plates, which can shift
the interference pattern.


-45° polarized light is on the slow axis of one birefringent quarter-wave plate and on
the fast axis of the other quarter-wave plate. This means a +90° degrees phase shift
on the path of the first one and a -90° degrees phase shift on the path of the second
one. The total relative phase shift is 180° which causes the entire interference pattern
to shift by 180° Regards, Hans

 

[JesseM]

There's a very distinct difference between the usual EPR experiments with a Wollaston prism
and this experiment:

The angle of linear polarization of the photons explains all the results.

This angle is what is used as the "Bohm hidden variable" in other EPR experiments where it
fails to explain the experimental results.


Regards, Hans

But classical linear polarization can have a continuous set of angles, while the linear polarization detectors always give one of two results (labeled x and y on the chart in the 'Which-Way Marker' section of http://grad.physics.sunysb.edu/~amarch/ ), and likewise the circular polarization detectors always give one of two results (labeled L and R in that chart). If you're assuming the linear polarization angle is the hidden variable for the s photons, what are you assuming about the relationship between that variable and the result obtained by these two detectors? For a given linear polarization angle on an s photon, how do we decide whether the entangled p photon will give result x or result y? And for that same linear polarization angle, how do we decide whether the s photon will pass through slit 1 or slit 2 with the quarter wave plates in place? One thing that's clear from the chart is that if the entangled p photon gave result x, then if the s photon goes through slit 1 it must be measured to have circular polarization R and if it goes through slit 2 it must be measured to have circular polarization L, whereas if the p photon gave result y then this is reversed.

 

[LaserMind]

Surely an entangled photon cannot affect or 'act on' its partner, it is only correlated and even that is only a synchronisation of state observables wrt time. If bob is observed as an x then alice instantly becomes a y?

 

[LaserMind]

http://grad.physics.sunysb.edu/~amarch/
Under 45 (or -45) degrees they both produce linear polarized light. Either both horizontal
or both vertical light. Figure 4 therefore corresponds with one of the two interference
patterns adding up to the "non-interference" pattern of Figure 3.

Regards, Hans

Exactly, and there are some claims that lack of interference pattern is due to 'which way' information whereas its due to two normal interference patterns that have been added.

 

[Hans de Vries]

But classical linear polarization can have a continuous set of angles, while the linear polarization detectors always give one of two results (labeled x and y on the chart in the 'Which-Way Marker' section of http://grad.physics.sunysb.edu/~amarch/ ), and likewise the circular polarization detectors always give one of two results (labeled L and R in that chart). If you're assuming the linear polarization angle is the hidden variable for the s photons, what are you assuming about the relationship between that variable and the result obtained by these two detectors? For a given linear polarization angle on an s photon, how do we decide whether the entangled p photon will give result x or result y? And for that same linear polarization angle, how do we decide whether the s photon will pass through slit 1 or slit 2 with the quarter wave plates in place? One thing that's clear from the chart is that if the entangled p photon gave result x, then if the s photon goes through slit 1 it must be measured to have circular polarization R and if it goes through slit 2 it must be measured to have circular polarization L, whereas if the p photon gave result y then this is reversed.

The point is that they do not use the standard interference rules for a massless vector field
where components under 90° do not interfere (H and V). Instead they seem to confuse it
with the interference rules for a spinor field where spin-up and spin-down states do not
interfere.

The classical EM field rules are good enough to determine the interference pattern since
the QED propagator for the photon field (1/q^2) is classical. A (more or less) 50:50 mixture
of L and R circular polarized radiation gives linear polarized radiation so one should not
expect to measure circular polarized photons and be able to obtain which-way information.Regards, Hans

 

[jambaugh]

True, but this will still not tell you, whether there is no interference pattern due to entanglement or whether the light is just extremely incoherent.

You can view that extremely incoherent beam as "entangled with the environment". I think there is some virtue in viewing entropy as entanglement with the environment.

 

[DrChinese]

Well that's very outspoken. Let's study the experiment then and go through it step by step:

Classical optics tells us that:

1) +45° linear polarized light will produce an interference pattern.
2) -45° linear polarized light will produce an interference pattern displaced by 180°
3) A mix of arbitrary linear polarized light will produce no interference pattern

Why do you think this is wrong from a classical optics point of view?

Regards, Hans

Classical optics does not feature entangled waves. Yet wave entanglement can be demonstrated - in an EPR setup, the waves must show perfect correlation. Provide an explanation of that behavior and we will have a good starting point to discuss the next hurdle.

Obviously, we are simply heading down the path of Bell... and we already know where that leads. So that is why I made my "bold" statement. It does not make sense to offer a model that has already been experimentally excluded. No quantum eraser model is going to be viable for a model which cannot pass a Bell test first.

I am not trying to be contrary, just saying that you cannot ignore Bell in this situation.

 

[DrChinese]

Surely an entangled photon cannot affect or 'act on' its partner, it is only correlated and even that is only a synchronisation of state observables wrt time. If bob is observed as an x then alice instantly becomes a y?

I would say that is the question, and the answer is not known. But you cannot assume this to be true.

 

[LaserMind]

I would say that is the question, and the answer is not known. But you cannot assume this to be true.

Dr C -
hmmm, can you give me a reference(s) to experiments or theorems that indicate otherwise? Sounds like a UFO hunt to me, but I am eager to dig into it and change my opinion.

 

[JesseM]

Dr C -
hmmm, can you give me a reference(s) to experiments or theorems that indicate otherwise? Sounds like a UFO hunt to me, but I am eager to dig into it and change my opinion.

You could take a look at Bohmian mechanics, an interpretation of QM which makes all the same physical predictions as any other version of QM, but which features hidden variables that can influence one another instantaneously at a distance.

 

[DrChinese]

Dr C -
hmmm, can you give me a reference(s) to experiments or theorems that indicate otherwise? Sounds like a UFO hunt to me, but I am eager to dig into it and change my opinion.

JesseM correctly points out Bohmian Mechanics (BM, also referred to as de Broglie Bohm or dBB). In this view, the state of particles that are non-local to the entangled particles themselves provide critical influences that are intended to describe and explain the entanglement mechanism. Some groups of scientists have studied this concept in depth. While the ideas are still imperfect, the basic Bohmian programs are able to reproduce the testable essentials of QM. However, there is no relativistic version yet and there is no "one" version of BM as there are competing versions.

You can also imagine that there might be force carriers, previously unknown and with no other known footprint, which have the ability to travel FTL. Perhaps these are exchanged between entangled particles. This, of course, would be pure speculation and there is no evidence whatsoever to support the view... but it is possible.

Either way, it is *possible* that non-locality is a part of nature.

 

[Dbar_x]

May I offer a criticism of the Walborn, Padua experiment? Note carefully that the two terms superposed in equation 2 describe the probable results of a measurement of the compound object, composed of a photon (described by psi) and the which-path marker (described by M). The authors show that results of a measurement of the compound (for emphasis, COMPOUND) system, specified by QM as the absolute square of Psi (that’s capital Psi, the left side of equation 2), include no cross terms, indicative of no interference. Again, carefully now, this means that if one measured the compound system with some as yet unspecified apparatus, that compound system would not exhibit interference. It would have no interference because the eigenfunctions of M are orthogonal.

But it’s not an interference pattern of the compound system that is supposed to disappear and then be restored via quantum erasure. Instead, the interference pattern of a single photon, described by psi, is what we are interested in. It is absolutely not the case that because a compound object exhibits no interference, then its constituent systems will also exhibit no interference. (For simplicity, this is like an exploding artillery shell, composed of fragments. We cannot tell where each fragment went by looking at the center of momentum of the entire shell. The compound object doesn’t tell us everything about each constituent. The single photon wavefunction, psi, determines everything about the photon, not the compound wavefunction, Psi.)

The implied inference the authors give us, that the photon interference is gone, is incorrect, and misleading. It’s no surprise, then, that if the interference never disappeared, it can be made to reappear.

It seems to me that we ought always to keep in mind, when discussing quantum erasure, the original theoretical analysis from 1978 that has generated all these QE experiments over the years. (Sculley, et al., Phys. Rep. 43, p. 485) (Am I actually the only person who has read that article carefully?) Scully and his colleagues meticulously described the quantum mechanics for a heavy molecule of spin one-half traveling through a modifoed Stern-Gerlach magnet. They placed a measuring apparatus, in this case a bi-level atom, in one arm of the magnet. They say that if the molecule goes that way, it will always kick the atom into its excited state, thus measuring which path was taken.

They use Schrodinger’s equation, of course, to show that after passing through the magnet, the density matrix for the molecule-atom system will be almost diagonalized. Meaning that the off-diagonal terms are small compared to terms on the diagonal. (That’s not really a diagonalized matrix, by the way.) Their analysis depends on the crucial assumption that because the molecule is arbitrarily heavier than the atom, there will be an arbitrarily small momentum transfer to the spinning molecule. This, they assert, implies no “significant” change to the molecule’s wavefunction at measurement, so continuous Schrodinger evolution continues, they claim.

But, consider this: no matter how heavy the molecule is, it always kicks the atom from ground to its excited state. That’s a definite quantized energy. Energy is conserved, so the molecule always loses that same quantum of energy. Each distinct, total energy state of the molecule is specified by a unique, linearly-independent eigenfunction. Each such eigenfunction specifies a distinct, independent, measured state of the molecular system. So, this claim we often hear, that the measurement did not disturb the object measured, is not justified by this analysis.

Scully et al. then imply that since the molecule’s wavefunction evolved continuously through measurement, we ought to be able to reverse that evolution by reversing (erasing) the state of the atomic detector. That’s what was meant, initially, by quantum erasure. Thus, disappearance of interference, evidence for a measurement, is supposed to be restored by returning the apparatus to its ground state. But it’s not a credible physical theory.

I realize that those who’ve advocated for quantum erasure have changed its meaning over the years, as successive experiments have proved unpersuasive. We now hear of object-apparatus entanglement, and sub-ensemble sorting. But, if the theory is not consistent and comprehensible, its not scientifically sound.

DocMike

 

[JesseM]

I realize that those who’ve advocated for quantum erasure have changed its meaning over the years, as successive experiments have proved unpersuasive. We now hear of object-apparatus entanglement, and sub-ensemble sorting.

Object-apparatus entanglement? Where do we "now hear" of that? If you're referring to my posts on the "Interference seen in a member of an entangled pair" thread, you didn't read very carefully: I made it quite clear that object-apparatus entanglement would only be necessary to analyze a wholly impractical thought-experiment where a macroscopic apparatus can remain completely isolated from the environment for a long period of time (long enough that if you measure it at an earlier time you will gain which-path information, but if you measure it at a later time it will give you no which-path information), akin to the Schroedinger's cat thought-experiment. In practical quantum eraser experiments, the "marker" that has the potential to give you which-path information (unless it is measured in such a way that this information is 'erased', or if you prefer, never existed, which as I said in post 56 here is just a semantic issue) is just another entangled particle, like the "idler" that can give you which-path information for the signal photon in the delayed choice quantum eraser. There is no need here to imagine that the measuring apparatus becomes entangled with what it measures, the assumption that measurements collapse the 2-particle wavefunction should work just fine. If you know a practical quantum eraser experiment where the authors felt the need to assume the measuring system becomes entangled with the particle being measured, please point it out.

 

[Dbar_x]

Object-apparatus entanglement? Where do we "now hear" of that?

Mohrhoff's article in the American Journal of Physics in 1996 was the most pointed criticism of quantum eraser theory that I know of. The response of Scully and his colleagues was, it seems, to find a different meaning for quantum erasure. They did some calculations, not entirely persuasive, which led to an explanation involving entanglement and the sorting of coincidence measurements into sub-ensembles. One sub-ensemble correlated with interference, the other sub-ensemble with no interference.

DocMike

 

[JesseM]

Mohrhoff's article in the American Journal of Physics in 1996 was the most pointed criticism of quantum eraser theory that I know of. The response of Scully and his colleagues was, it seems, to find a different meaning for quantum erasure. They did some calculations, not entirely persuasive, which led to an explanation involving entanglement and the sorting of coincidence measurements into sub-ensembles. One sub-ensemble correlated with interference, the other sub-ensemble with no interference.

What do you mean by "sub-ensembles" in this context? And what does this have to do with entanglement between the particles and the measuring apparatus? If these papers are not available online, perhaps you could quote a relevant paragraph or two?

edit: The ensemble interpretation of QM interprets the wavefunction as just giving statistical predictions about experimental results on an ensemble of trials where the system is prepared in the same initial state and measured the same way. So are sub-ensembles just the theoretical analogue of a coincidence count, like the probability the signal photon will be detected at different points on the screen given the assumption that we're looking at the subset of trials where the idler was detected at, say, detector D2?

 

[p764rds]

Wheelers delayed path does not require backwards in time theories provided we use the CI approach. If its presented as a typical wave particle conundrum then all types of horrors emerge (read Wheeler's analysis) - I am expecting the same of the Quantum Erasure claims by Scully and am requesting a re-evaluation.