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What Is the Quantum Eraser Thought Experiment?

Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.

Changing Causality

So, in my prior article on the quantum delayed choice experiment, we finally have established that quantum mechanics is indeed a real phenomenon though many experiments. But we haven’t yet figured out if quantum experiments themselves disturb quantum systems so that we only spot particle or wave properties as we have seen. We cannot spot both particle and wave information at once because of the experimental rig, not because of underlying properties (113).

For quantum scientists such as Bohr, the uncertainty principle prevents such problems because knowing one really well means we cannot know the other as well regardless of our setup. The behavior of one causes the other to disappear. However, delayed choice experiments have shown that the behavior of a particle will net the same result despite the order in which we run the photon through. The physical alignment does not impact the behavior seen, so our rigging is independent of quantum mechanics. So what gives? (Ibid)

Enter the delayed-choice quantum eraser thought experiment by Marlan Scully and Kai Druhl, in which an entangled photon passes through double slit and the information of the path it takes is recorded via the behavior of the other photon and so no interference pattern is possible. But what if I erased that information before reading it but after the photon had travelled through the slits? Would the interference pattern return, a transition from a classical state to a quantum state? (114-6)

That would be interesting because the collapse is the quantum to classical, therefore a reversal would be anti-causal. A photon that has travelled across the Universe for billions of years could have its behavior retroactively changed retroactively depending on how I chose to measure it (Ibid).

The actual set-up is a bit more complicated to establish, and it involves several beam splitters and detectors. We first of all have two atoms (which act like a proxy double-slit) that emit their own pair of photons, with one member of each pair going to a screen and the other to our interferometer. We will have photon A going towards its beam splitter (BSA) while photon B goes to its own (BSB). At BSA, photon A can either pass through to detector 1 (D1) or be reflected on, while photon B can go to detector 2 (D2) or also pass through. These photons, if reflected on, will then encounter a common beam splitter (BS) and either pass through or reflect to our final detectors (D3 or D4). If either D1 or D2 fire off, we know with 100% certainty where photon A and photon B went and so no interference pattern is possible (Ananthaswamy 117-120, Sweatman).

However, D3 and D4 will be trickier to talk about and in fact we would need additional information to uncover our photon’s destinations, and that could come from the photons that hit the screen. However, those photons created an interference pattern because until we measure them offer no way to identify their origin. So if we measure the screen we can tell which photons hit D3 and D4, and we can delay that choice for as long as we want to, or let the information remained erased (Ibid).

The experimental set-up visualized.

The experimental set-up visualized.

And if the experiment itself is difficult to conceptualize, it’s even trickier to test and yet it was, by a team with Scully on board. It involves the basic set-up from before, with a crystal being the source of entangled photons as it is hit by a prior photon emerging from one of our double slits. One of the entangled photons goes to a detector while the other enters our beam splitter set-up, but which path taken is unknown and depends on which slit the photon exited and where it hits the prism. If entering the beam splitter system, each path will encounter a beam splitter to either reflect it out of the system or allow it to be transited. A master beam splitter is placed in between the two possible transmitted paths and thus generating the wave pattern from the interference of the two paths. The information about what went where is sent to a coincidence circuit to be recorded. That initial photon that never entered the system was shown to have its choice affected by whether I preserved the information or allowed to pertain despite the fact that it hit a detector before the photon entering the beam splitters did! (Kim, Gaasbeek)

Another confirmation was done by Zeilinger in the Canary Islands. Space is the big issue here, and a lack of interference crucial too. One site was at La Palma mountain (housing the a Mach-Zehnder interferometer) while the other was at Tenerife (where one of our photons is received), a total distance of 144 kilometers (which as we will see is crucial to eliminate space-like influences courtesy of relativity, ensuring that nothing should happen). Unlike the theoretical 2 atom set-up from Scully, this used a single source of entangled photons with one being sent to Tenerife and the other to the interferometer. Our beam-splitter is different here too, not just reflecting light but directing it based on the polarization of the photon. This is a layer of information that can be erased, for if we know the polarization of the photon then we know its direction as well (and vice-versa) (Ananthaswamy 121-7).

But recall the entanglement we established between photons. The polarization of one will impact the other as well, so if we erased that information then we could have a delayed choice scenario where the detected photon would then alter its behavior. The distance between Tenerife and La Palma contributes to this, making the delayed nature easier to spot but also required sensitivity measures like using a piezoelectric crystal (whose length changes depending on the voltage running through it), measuring wind speeds, temperature gradients, and laboratory vibrations minimized. They even had to run the rig at night to minimize photonic noise. Even a moon-lit night would be too much! (Ibid)

As far as deciding when to/not to erase the information, a random number generator was used. If a zero was found then the original polarization was maintained but if a one then it would be scrambled and hence erased. So, if a zero then we knew D1 (horizontal polarization) or D2 (vertical polarization) would get their hits but if a one then a 50/50 shot of landing at D1 or D2 was created. The decision to erase or not to was made 0.5 milliseconds after the photon traveled through the interferometer and made contact with a detector. It was found that when the Tenerife photon was measured, the detectors had their particle hits as expected, but when the information was erased then the wave behavior would return despite the delayed choice in choosing to erase the information (127-8).

This is fascinating, though admittedly complicated. What this delayed choice quantum eraser experiment confirms is our interpretation of reality needs adjusting, and it looks like time will be the guilty party. Those La Palma photons shouldn’t be altered because that choice was made post-interaction, and the choice to do so was random and not even by intent. We can see this wave-particle duality, the properties of entanglement, and the death of hidden variables via the violation of the Bell Inequality. But now, what does this do to our idea of measuring something if causal links can be violated? What does a collapse into a state even mean? (128, 131-2)

We claim it happens because statistically it’s likely but no physical theory can fully account for it. In fact, we can see that traditionally physical theories will not be enough here. Maybe instead we need to consider wild ideas, like a chain-wave progression of entanglement-induced collapse, but then again quantum erasing could counter this too. Consider an electron which is a piece of an entanglement chain, and upon being hit by a photon causes it to rise in orbital, thus breaking the entangled state. But another photon could strike the atom, rendering the electron unable to make such a change and so the data is erased and the collapse never happens (Ibid).

Quantum Bombs

So, now that I have messed up your notions of causality, there are still further issues that we have skimmed over. What really is a measurement? What is the boundary (if any) between classical and quantum mechanics? When the wave function collapses, what does that even mean? Is the wave function even real or just a mathematical tool approximating something more? (133)

Lev Vaidman and Avshalom Elitzur took a look at the measurement issue from a new stance. They wondered if quantum mechanics could be used to find objects without interacting with them. From a classical viewpoint this is nonsense, but we are not playing with those rules here. Using an interferometer with vastly different arm lengths (where the reflected photon hits detector 1 close by but the transmitted detector is far, far away), we can see that if D1 registers a hit then nothing made it to D2, but if we don’t hear from D1 then I know it went to D2 without having to measure it, courtesy of that huge distance guaranteeing the photon’s trip after a given time value. We have caused a collapse of our state with an “interaction-free measurement” (134).

A rigged quantum bomb experiment.

A rigged quantum bomb experiment.

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Now, let’s up the ante. Vaidman and Elitzur took this further and developed their bomb problem. Yes, they found a (theoretical) quantum rigging for a bomb that employs a single photon as the trigger. You see, bomb manufacturing inherently has defects and we would love to test out the bomb in a manner that isn’t dangerous to us. We need a way to interact with it and measure a value about it. Bring in a Mach-Zehnder interferometer, with a bomb placed past the 1st beam splitter but before the 2nd one. If the 1st detector goes off then we know the bomb is bad because it didn’t go off and so we have wave behavior courtesy of the lack of engagement, causing the superposition of states to only allow detector 1 to go off (Ananthaswamy 135-140, Gidney).

But what about other possibilities? Turns out, three other possible scenarios can occur. In one scenario the photon went down the path of the bomb and triggered it. In another, it travelled down the other path and encountered the 2nd beam splitter, therefore potentially going to either detector. If it hits detector 1, then we would think it was the dead bomb scenario by mistake, but if it went to detector 2 then we know its live because that is the only way such a detector can go off. It can be confusing because it would seem then because I measured the detector then the bomb should collapse too, but remember that by interacting with the bomb the photon’s superposition extended to the bomb also. By hitting the second detector, the system collapses without the photon engaging with the bomb (Ibid).

Altogether, for any given detection, we have a 50% chance of a straight dud, a 25% chance of a live mistaken for a dud and a 25% chance of a live bomb. We achieved our measurement without directly collapsing the object, but the inherent “nonlocality and randomness” built into it troubles people (as it should). Collapsing states must therefore employ something more than a measurement, right? (Ibid)

Lucien Hardy looked into this when he considered a purely quantum-based bomb as opposed to a classical one with a photon trigger. To achieve this, we would need two Mach-Zehnder interferometers that seemingly overlay portions of their paths onto the other, allowing for the possibility of particles to interact with each other. One interferometer used an electron while the other uses a position. These are matter/antimatter partners and upon contact explode in a great burst of energy. Our interferometers are aligned to allow for a potential particle hit before reaching the reflective mirrors of each rig. Remember, this is just allowing for the possibility of a hit, not a certainty. In the single interferometer arrangement, one detector would go off because of constructive interference and the other fail because of destructive interference, so we will call our detectors C+, D+, C-, and D- (the signs indicating electrons vs. positrons) (Ananthaswamy 140-143)

But if our particle’s paths cross, then things can get a little…complicated, and the wave nature can disappear because of superpositioned states collapsing each other, just like in the bomb scenario. Our electron would have wave behavior only if the position goes down the non-interacting route between the two particles, and vice versa. There would be no way for them to superimpose and cause a collapse between them as a result of entangled states (Ibid)

But what if we wanted particle behavior? When our particles enter that potential interacting route, we get a bomb scenario once again but with the positron informing me of the electron’s route. The electron has a 50/50 shot of going down each path. If they both go down at same time then they cancel each other out but if the electron took the non-interacting route then it goes to either C- or D-. If D-, then it has to be a particle because the wave is canceled out for that detector, meaning only a particle hit can set it off. After all the math is done, Hardy found just a 1/16 chance of both D+ and D- going off at once (Ibid).

But…that is a major problem. You see, we knew that information about D- because the positron went down the interacting arm. If D+ were to go off, the electron had to go down its interacting arm. Both particles should collide and cancel each other out, meaning the chance should be 0 instead. Dirk Bouwmeester and his team tested our Hardy’s Paradox using photons and polarizations. This was done because the technology for the electron/positron rigging wasn’t possible at the time. After making all the necessary adjustments and running the experiment, they indeed found the calculated probability was the actual one, despite how it should be 0. As if we need it to be stated, but once again quantum mechanics proves how it defies classical mechanics in its nonlocal behavior courtesy of entanglement. Perhaps our ideas of measurement need some revising, also (143-4).

A Brief Note

It is worth briefly mentioning that not all quantum physicists are on board with this interpretation of results. Sean Carrol points out that retrocausality doesn’t have to be the main takeaway here, but instead could be seen as evidence for the Everett Many Worlds Interpretation of quantum mechanics. In this oversimplified statement on the topic, it states that each choice possible to the Universe branches out and fulfills its own destiny, fully realized (Carroll).

That these eraser experiments seem to make retrocauslity a reality is just the misinterpretation of the Everett state we are in, with other Universes failing to find such a correlation because of how we entangled the particle by removing it from the universal system. We can have many different measuring techniques that don’t have to be consistent with each other, he argues for. If we want to see a true behavior of this phenomena, we need to decohere from a wider system and go from there. The results could also be seen as evidence for anti-realism, removing the definite states that quantum objects can have until they are observed (Ibid).

Be sure to check out more of my articles as we will continue to explore other topics in this field such a Bohemian Mechanics. Quantum physics is difficult, so thank you for your patience with this article. I hope it was beneficial for you and perhaps will inspire you to pursue this topic even further. I will leave you with these thoughts from Lee Smolin which exemplifies my feelings on not just this topic, but on life itself.

It helps with understanding these topics by reminding us about why they fascinate us. “To have a scientific mind is to respect the consensus facts, which are the resolution of generations of disputes while maintaining an open mind about the still unknown.” We need to keep the importance of the “sense of the essential mystery of the world,” that as we learn more about everything even more mysteries will crop up. It should give us a “sense of wonder and gratitude just to be a part of it all.”

Works Cited

Ananthaswamy, Anil. Through Two Doors at Once. Random House, New York. 2018. Print. 113-128, 131-144.

Carrol, Sean. “The Notorious Delayed-Choice Quantum Eraser.” Preposterousuniverse.com. Sean Carrol, 21 Sept. 2019. Web. 18 Feb. 2020.

Gaasbeek, Bram. “Demystifying the Delayed Choice Experiments.” arXiv:1007.3977v1

Gidney, Craig. “Quantum Bomb Detector Detectors.” Algassert.com. Algorithmic Assertions, 11 Feb. 2017. Web. 18 Feb. 2020.

Kim, Yoon-Ho et al. “A Delayed Choice Quantum Eraser.” Bottomlayer.com. Bottom Layer, 04 Sept. 2002. Web. 18 Feb. 2020.

Sweatman, Will. “The Quantum Eraser.” Hackaway.com. Hackaday, 07 Sept. 2016.Web. 18 Feb. 2020.

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

© 2021 Leonard Kelley

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