# Delayed Choice Quantum Erasure- Changing the Past?

*Most recent answer: 01/12/2014*

- Kenny (age 28)

London, UK

Hi Kenny,

Short answer: "there would be an interference pattern on the back wall if it is later decided to not look at the information right?" Actually not. If you don't look at the information, there is not an interference pattern. To recover the interference pattern, you have to actually measure the which-way information in a "diagonal" basis, and then only keep particles with a specific outcome in this basis.

Long answer: I'll start with an overview of the experiment you refer to, for readers who are less familiar or have slightly different questions on the same topic of delayed choice quantum erasure in a double slit experiment.

Start with the double slit experiment: individual photons of, say, horizontal (H) polarization, are sent through two slits. If we don't label which slit each photon went through, then we see an interference pattern on the output screen. If, however, we put a waveplate over one slit which rotates the polarization of photons to vertical (V), then we have labeled photons passing through that slit. (By testing to see if the light is H or V, we can tell which slit the light passed through.) Because we have labeled the slits, we lose the interference pattern.

This last fact is true even if no one *actually does* the H/V measurement. This is mostly easily seen if you do the calculations for classical light, made of electric and magnetic field vectors. The polarization vectors H and V are perpendicular, so even if they are out of phase, they don't point in opposite directions, so they never cancel each other, and you never get interference minima. The calculations are a bit harder for single photons, but you can get the exact same result by writing the full quantum states in terms of density matrices. To recap: the mere existence of "which-way" (WW) information completely destroys the interference fringes.

Now, a natural question to ask is, can you get rid of the WW marker (in this case the polarization difference for light passing between the two different slits) and restore the interference? In our experiment, you could place a polarizer right before the screen at a diagonal angle between H and V, which would pass half of the photons, and change all of their polarizations to diagonal (D). After this polarizer, photons passing through either slit are totally indistinguishable, so, sure enough, interference is restored.

All this so far is fascinating by itself, but can be extended to seem even more crazy. I'll leave out some details, though a fantastic and full description of everything I've said can be found in this journal article: ("Quantum Erasure: In quantum mechanics, there are two sides to every story, but only one can be seen at a time. Experiments show that "erasing" one allows the other to appear," by Walborn and Monken)

Here's the basic idea, and I'm finally getting to your question, Kenny.

Instead of labeling which slit each photon takes using its own polarization, imagine storing that information on another, separated particle's polarization. This can be done using an entangled pair of photons in the state H_{1}H_{2} + V_{1}V_{2}. Now, you send particle 1 to Alice, and you send particle 2 through Bob's two polarization-labeled slits. Now, you may have heard that Alice can choose to measure particle 1 in the H-V basis, in which case Bob doesn't see fringes, or she can measure in the D-A basis, in which case Bob sees the fringes, just like in the quantum erasure case above.

This is NOT true, but let's think about what it would mean if it were. If this were possible, then Alice and Bob could live on opposite sides of the universe and send instantaneous messages as strings of 1's and 0's by choosing "fringes" to mean a 1 and "no fringes" to mean a 0, for example. Instantaneous messaging is not allowed by relativity. Furthermore, as Kenny suggests, such a scheme could be used to send messages to the past, which also leads to huge paradoxes.

Here's how the experiment above, the so-called "delayed choice quantum eraser," *actually* works. Alice can choose to measure either in the H-V or the D-A basis. In the first case, she randomly gets either an H or a V. In the second case, she randomly gets either a D or an A. Meanwhile, Bob looks on a screen after his two slits.

After they repeat the experiment with a few million single photon pairs, he never sees an interference pattern, no matter what Alice does. So, Alice has no way to send messages instantaneously, or to the past.

What Alice and Bob *can *do, however, is meet up later and compare results. If Alice tells Bob each of the photons which she found to be H, Bob can look at the pattern only for his corresponding pairs, and he won't see anything interesting; same for pairs which Alice found to be V. If Bob only plots photons whose partner Alice found to be D, however, then Bob **will** see fringes! If he only plots photons whose partner Alice found to be A, then Bob will see "anti-fringes," which are just fringes shifted by 180 degrees.*

This is always how quantum erasers work... you have to "post-select" particles with a specific outcome (e.g. D) in the diagonal basis (e.g. the D-A basis). It's basically just clever book-keeping, nothing spooky. Furthermore, neither Bob nor Alice can predict if any individual particle will be A or D, so the best they can do to recover interference is to have Alice send a classical signal to Bob with the measurement outcome for each photon, after which he does the post-selection. This classical signal is limited by light speed, so even though the entanglement correlations are instantaneous, they don't by themselves carry any information.

Hope that makes sense,

David Schmid

*This all assumes that Bob doesn't do any measurement of polarization; the which-way information we care about is completely in the entangled partner that Alice has. If Bob does measure polarization, then he destroys the polarization-entanglement, and Alice no longer is relevant to Bob's results.

*(published on 01/12/2014)*

## Follow-Up #1: Measuring where a particle is... and isn't.

- Anonymous

Measuring where a particle is *not *going is a clever idea. However, it's been studied before, and I don't think there are any situations where it leads to new results or paradoxes.

The reason why nothing new happens is that getting a null measurement **does **collapse the wavefunction, just like getting a click on a detector. The easiest case to think about is if the particle has only two options, like in an interferometer... If you look in one port and don't see the photon, then you know for sure it is in the other arm.

Nonetheless, it is interesting (and possibly useful) to extract information by looking where particles aren't. There are some related ideas in the literature, for example interaction-free measurement and counterfactual processes, in which photons tell you information about objects with which they didn't interact. It's very counter-intuitive, but it's totally described by standard quantum mechanics.

You can find some great info by looking at or .

Cheers,

David Schmid

*(published on 03/30/2014)*