What is wrong with this method for FTL communication?

Question

I've seen the other questions, but almost all of them deal with manipulating quantum states so that the other person reads a message in the data. However, you cannot force a quantum state on something without breaking entanglement.

So here is my idea. I know that it can't work, but I don't know why. If someone could point out the flaw, I would appreciate it. I do not claim to be an expert.

So there is the double slit experiment. If I pass a single photon through a double slit, it will create an interference pattern. This is the evidence that it is in a quantum state because a single particle should not be interfering with itself. In reading article above, this also works my photon happens to be entangled with another photon.

Now in the quantum eraser section of the linked article above, it goes on to mention that if you apply a filter to one of the photons (i.e. measure it), than the interference pattern of both collapses. Thus, by measuring the quantum state of one, both collapse.

So, here is how I propose FTL communication.

Method

Lets say I create streams of quantum entangled photons. I will split up the pairs of quantum entangled photons and send one half to $A$ and the other half to $B$ in order. Thus, the first photon that $A$ receives will be entangled with the first photon that $B$ receives.

At $B$'s end, each photon will be run through the double slit to detect whether an interference pattern exists. If there was an interference pattern, then this is encoded as a binary $0$. If there isn't an interference pattern, then this is a $1$. It doesn't matter which slit the photon is known to travel through - the simple absence of the interference pattern is enough.

At $A$'s end, to communicate, I will encode my message in binary and then encode each bit in photon stream. If the next bit is a $1$, I will measure the next photon, thus collapsing its quantum state and eliminating the interference pattern. If the next bit is a $0$, I will not measure the next photon.

Example

$A$ needs to send 1101. $A$ would measure the first, second, and forth photons. At $B$'s end, when these photons are run through the double slit, you would see that the first, second, and forth have no interference pattern, so you would know they are $1$s. The third retains an interference pattern, so it would be a $0$.

Two-Way Communication

This allows $A$ to communicate to $B$ instantly. For $B$ to communicate back, you could create another set of streams where $A$ runs the photons through the double slit and $B$ measures to collapse the quantum state on some photons. Alternatively, odd numbered photons can be used for the reverse communication, so long as both $A$ and $B$ agree.

Summary

So, what is wrong with this method? It does not try to force a photon to go through a slit, but rather uses the act of observing or measuring to collapse the quantum state.

Answer 1

This has been answered before. I recommend not to read the question I link to, which is horrible, but the chosen answer, which is extremely well written and in accord with what I have heard our Professor for Quantum Optics say. Double-double-slit with entangled photons

P.S.: In general, on FTL communication: The crux is usually that entanglement is not as miraculous as it is thought to be. When you determine the state of one entangled particle at your end, it just means that you know which state the other one is in - but that's it! You can't SEND information, you just KNOW the state the other one is in. Same for the other end - he KNOWS now that your particle is the opposite of his, but neither of you could determine beforehand which state it would collapse into!

In your experiment the problem is, I think (and I'm not sure because I'm too tired), that interference would either show up in all cases or in none, so you couldn't choose at one station whether the other would measure interference or not.

Answer 2

I'm going to use electrons in place of photons because they have two options for their spin, but the problem is equivalent. The problem with the communication method is as follows:

You wanted 1 to be conveyed by A measuring the electron, 0 to be conveyed by A not measuring it.

Let's try to see what happens at B if A measures the electron. There is a 50% chance of A measuring spin 1/2, and a 50% of -1/2. What will B see? Well, there is a 50% chance that he sees of -1/2 (corresponding to A getting 1/2) and a 50% chance that he sees 1/2. A cannot control what the measurement will be, so A cannot control what value B will see.

What if A doesn't measure the electron? B is first to measure it. It has a 50/50 chance of spin 1/2 or -1/2.

The point: Even if A measures the electron, there is no measurable difference at B's location. In either case, B sees a 50/50 chance of +1/2 or -1/2. He doesn't know whether he is the first one to measure the particle or not. A cannot change the experimental outcome of measurement at B's location.

Answer 3

While the other two answers are technically correct, I believe the question hinges on a misunderstanding of what is really required to see an interference pattern in the first place.

The question implies that simply by not measuring the path of A through the slits, an interference pattern for B can be observed. The missing part of this scenario is that interference can only be observed as the sum of many observations. B will appear as a single dot on the detecting plate regardless of whether the path of A is measured or not. No single observation can be determined to fit either with an interference pattern or with the absence of one. After many observations where which-way information is not collected on many A's, many B's will have formed an interference pattern, however this is clearly not helpful if one's goal is communication.

What you'd actually observe on the detecting plate for B if you alternated measurement/non-measurement of A (expected to produce a 010101 in your proposed scenario) is a wide distribution of marks with no discernible interference pattern. Only by working backwards and time-correlating the B marks with the A marks that were not measured would you be able to pick out the interference pattern formed by those specific B's. The remaining marks on the detecting plate would NOT form an interference pattern, and would correspond to the times that which-way information was collected about A.

Of course, in order to time-correlate those measurements the folks running the A detector would have to share their data with the B detector scientists... no faster than the speed of light!