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bruce2g
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Delayed Erasure Demystified
Delayed choice quantum erasure experiments claim to produce a 2-slit interference pattern in a beam by 'erasing' the which-path information contained in an entangled beam. There's an implication that the erasure happens after the interference is measured, and that some sort of 'backwards time' phenomenon has occurred. I believe that if you look carefully at how the erasure is accomplished -- the two idler beams go through a beam splitter and onto two detectors -- then the normal direction of causality can be restored.
The basic argument is that you can look at the data and say that the erasure in the idlers brings out the interference in the signal photons (the authors' argument), or you can say that the X position of the signal photon determines the phase of both the signal and the idler, and this determines the probability that the idler will go to one or the other detector (my argument).
Basically, I'm going to make 4 points, and then elaborate on them.
MY POINTS
Point 1: In his delightful book "The Fabric of the Cosmos," Brian Greene describes the classic delayed choice quantum erasure experiment on page 196. Unfortunately, in his diagram, he oversimplifies the setup by omitting the coincidence counts between the signal detector D0 and and the idler detectors D1 and D2. This is a critical omission, because --
Point 2: The interference pattern only appears in the signal photons after the erasure if you discard half of the signal photons, and then look at the ones that remain. You have to either discard the signal photons which are coincident with idlers detected at D1, or else you have to discard those coincident at D2. Then you see the interference. This is why you need to (classically) combine the detection data of the signal photons with the detection data of the idler photons in order to see the interference.
The above points have been make on this forum before. I have 2 new points to make:
Point 3: Interference fringes show up as increasing and decreasing coincidence counts as a function of D0's x position behind the double-slit. The coincidence count is performed between D0 (the signal photon detector behind the slits) and either D1 or D2. As you move detector D0 (i.e., as you vary x), the coincidence counts with D1 go up and down to reveal an interference pattern. Similarly, the coincidence counts at D2 go down and up to reveal a complementary interference pattern. Figure 1 has a simplified diagram of the experiment.
There is another way to look at these data: you can also say that the probability that an idler is coincidence-counted at D1 is a function of the X position at which the signal photon is detected. As you vary X, the idlers will first tend to be detected at D1, but then the probability will move towards D2 as X increases, and then back to D1. This means that the beam splitter, which combines the two idlers and erases the which-path information, sends the combined idler beam photons to either D1 or D2 with a probability which depends on the X position at which the signal photon was detected. In other words --
Point 4: There is an entanglement between the signal photon's x and the idler's probability of registering at D1 or D2 (which is based on the relative phase between the idler beams when they reach the beam splitter). This is shown in figure 2. There, I have taken the data from the charts in the original article, and combined the D1 and D2 data using the following formula: for a given X, p(D1|X) = (D1 count when D0=X) / (D1 count when D0=X + D2 count when D0=X).
Thus, we see that the 'erasure' can be interpreted as another aspect of the entanglement (in this case the phase entanglement) between the signal and idler photons.
I mention these things because some people seem to think that the delayed choice quantum erasure experiment reaches back in time and somehow rearranges the signal photons into an interference pattern after the erasure at the beam splitter. This does not happen. If the signal photons are detected first, then you see the interference pattern emerge because the point at which a signal photon is detected determines the relative probability that the idler will subsequently be detected at D1 or D2.
References:
The Kim, Kulik, Shih and Scully experiment, is described in the paper 'A Delayed Choice Quantum Eraser' at http://xxx.lanl.gov/PS_cache/quant-ph/pdf/9903/9903047.pdf and also nicely annotated at http://www.bottomlayer.com/bottom/kim-scully/kim-scull
Bruce Zweig
Delayed choice quantum erasure experiments claim to produce a 2-slit interference pattern in a beam by 'erasing' the which-path information contained in an entangled beam. There's an implication that the erasure happens after the interference is measured, and that some sort of 'backwards time' phenomenon has occurred. I believe that if you look carefully at how the erasure is accomplished -- the two idler beams go through a beam splitter and onto two detectors -- then the normal direction of causality can be restored.
The basic argument is that you can look at the data and say that the erasure in the idlers brings out the interference in the signal photons (the authors' argument), or you can say that the X position of the signal photon determines the phase of both the signal and the idler, and this determines the probability that the idler will go to one or the other detector (my argument).
Basically, I'm going to make 4 points, and then elaborate on them.
MY POINTS
Point 1: In his delightful book "The Fabric of the Cosmos," Brian Greene describes the classic delayed choice quantum erasure experiment on page 196. Unfortunately, in his diagram, he oversimplifies the setup by omitting the coincidence counts between the signal detector D0 and and the idler detectors D1 and D2. This is a critical omission, because --
Point 2: The interference pattern only appears in the signal photons after the erasure if you discard half of the signal photons, and then look at the ones that remain. You have to either discard the signal photons which are coincident with idlers detected at D1, or else you have to discard those coincident at D2. Then you see the interference. This is why you need to (classically) combine the detection data of the signal photons with the detection data of the idler photons in order to see the interference.
The above points have been make on this forum before. I have 2 new points to make:
Point 3: Interference fringes show up as increasing and decreasing coincidence counts as a function of D0's x position behind the double-slit. The coincidence count is performed between D0 (the signal photon detector behind the slits) and either D1 or D2. As you move detector D0 (i.e., as you vary x), the coincidence counts with D1 go up and down to reveal an interference pattern. Similarly, the coincidence counts at D2 go down and up to reveal a complementary interference pattern. Figure 1 has a simplified diagram of the experiment.
There is another way to look at these data: you can also say that the probability that an idler is coincidence-counted at D1 is a function of the X position at which the signal photon is detected. As you vary X, the idlers will first tend to be detected at D1, but then the probability will move towards D2 as X increases, and then back to D1. This means that the beam splitter, which combines the two idlers and erases the which-path information, sends the combined idler beam photons to either D1 or D2 with a probability which depends on the X position at which the signal photon was detected. In other words --
Point 4: There is an entanglement between the signal photon's x and the idler's probability of registering at D1 or D2 (which is based on the relative phase between the idler beams when they reach the beam splitter). This is shown in figure 2. There, I have taken the data from the charts in the original article, and combined the D1 and D2 data using the following formula: for a given X, p(D1|X) = (D1 count when D0=X) / (D1 count when D0=X + D2 count when D0=X).
Thus, we see that the 'erasure' can be interpreted as another aspect of the entanglement (in this case the phase entanglement) between the signal and idler photons.
I mention these things because some people seem to think that the delayed choice quantum erasure experiment reaches back in time and somehow rearranges the signal photons into an interference pattern after the erasure at the beam splitter. This does not happen. If the signal photons are detected first, then you see the interference pattern emerge because the point at which a signal photon is detected determines the relative probability that the idler will subsequently be detected at D1 or D2.
References:
The Kim, Kulik, Shih and Scully experiment, is described in the paper 'A Delayed Choice Quantum Eraser' at http://xxx.lanl.gov/PS_cache/quant-ph/pdf/9903/9903047.pdf and also nicely annotated at http://www.bottomlayer.com/bottom/kim-scully/kim-scull
Bruce Zweig
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