What is information?

[Vertigo 7]

I'm by no means an expert in quantum physics, but doesn't quantum entanglement allow for communication over any distance with out waiting on travel time?

As I understood the basics and the practical application, the entangled pair could be on opposite sides of the universe and manipulating the electron spin of one half would impact the other, essentially allowing binary communication between the two pairs with no lag time between them.

Correct me if I'm wrong, but with that, wouldn't it be possible to get around the speed of light for FTL communication? We would just need more portable devices to measure electron spin and manipulate it to be practical.

[pjknibbs]

The problem there is that you're talking about measuring a quantum property of a particle, and quantum measurements are essentially random. Or, to put it another way, there's no way to guarantee that the state of the particle will remain the same in between the remote one being changed and you measuring the one at your end. When people are testing out quantum entanglement they're using very precise clocks to ensure the two measurements are taken at exactly the same time, which would not be possible if you move the two particles a long distance apart.

[Vertigo 7]

I swear i remember reading an article where they were suggesting using quantum entanglement for a device that would effectively be a cell phone for secure communications but the only limitation was portability and production costs since communication would only work between the entangled pairs. But that was many moons ago and isn't something I actively follow.

[red assassin]

You're talking about two different things here. Yes, there is interest in quantum mechanics for communication, but not for speed reasons. I'll talk about that in a bit - first, why you can't communicate with quantum entanglement.

Consider the following scenario: You, Alice, have a set of spin 1/2 particles (this means they can be spin up or spin down), each of which is entangled with a pair particle held by Bob. This means that, if you measure one of your particles and find it to be, say, spin up, then when Bob measures the pair to that particle, he will find it to be spin down. (We can call these states, say, 0 and 1, for comparison with classical information theory.) Until measured, each of those particles exists in a superposition of the two states, but the instant one party makes a measurement, it's guaranteed that the pair particle will be measured in the other state, even if information communicating this couldn't possibly have travelled between the two in time. So far, so good.

However. Let's say you measure one of your particles. You get spin down. Then you measure another one of your particles. You get spin down as well. So what? Has Bob measured one or both of those particles? You don't know. When you send a classical, speed-of-light-constrained message to Bob, you can find out which ones he's measured and that for the ones he's measured, he's measured the other state to you as expected. But no information has been exchanged until you do that. You don't have any ability to affect the measurements made by the other party without exchanging classical information; all that happens is that the two sets of measurements, when compared, will be found to match.


So, quantum mechanics in communications. Most probably you've heard of quantum cryptography. There's a few different things under this umbrella, but quantum key distribution is the most common. This can be implemented using entangled particles, but I think the implementation without is a bit easier to follow, so I'll use that (the protocol I'm using here is BB84). We're Alice, and we want to transmit some random sequence of bits to Bob, so we can use it as a cryptographic key. We want to know if somebody is listening to our communication when we do this. Here's what we do:

First, we set up the ability to transmit particles to Bob. Once again I'll use simple spin 1/2 particles.
Second, we generate some random string of bits. This needs to be twice as long as the key we eventually want to share.
Third, we transmit it bit by bit to Bob. We do this by encoding it into the particle spin. However, we're going to vary the way we do this: for some of the particles, we'll make spin up 1 and spin down 0, but for other particles we'll make spin right 1 and spin left 0. There's nothing weird about this, it's just a case of which axis (vertical or horizontal) we measure the spin in. However, we don't tell Bob which particles we've used which axis for.
Fourth, Bob receives these particles. Because he doesn't know which axis we've used for each, he just guesses, and records the results. For the ones where he guessed right, he'll get the same bit we had; for the ones he guessed wrong, he'll just get a random value.
Fifth, Alice and Bob both tell each other what axis they measured each particle in. They ignore the ones where they used different axes. For the ones where they measured them in the same axis, they'll have the same value. This forms their key, which they can then use to communicate, safe in the knowledge that there was no eavesdropper. Why?

Because a measurement in one axis destroys information about the value set in another axis. That is, if Alice encodes a bit in the vertical axis and sends it to Bob, and Eve measures it in the horizontal axis, not only will she get a random value, but the information Alice encoded in the vertical axis is gone. When Bob measures, even if he measures it in the vertical axis like Alice did, he'll get a random value. Since Eve doesn't know the axes to use and is guessing at random like Bob, she'll inadvertently destroy the information encoded in half the particles. When Bob and Alice then try and communicate using their shared key, they'll find they can't, which tells them there was an eavesdropper.


You can do the same thing using measurements of preshared entangled particles rather than transmitting the entangled particles around, but establishing the key still requires Alice and Bob to classically tell each other what axes they made the measurements in, so it's still constrained by the speed of light.

Also note that this algorithm doesn't prevent Eve from man-in-the-middling the communication (i.e. setting up separate communications with both Alice and Bob, decoding everything and re-encoding it and transmitting it onwards), it just stops her passively intercepting the information. A separate authentication protocol is still required.

[Bishop149]

Consider the following scenario: You, Alice, have a set of spin 1/2 particles (this means they can be spin up or spin down), each of which is entangled with a pair particle held by Bob. This means that, if you measure one of your particles and find it to be, say, spin up, then when Bob measures the pair to that particle, he will find it to be spin down. (We can call these states, say, 0 and 1, for comparison with classical information theory.) Until measured, each of those particles exists in a superposition of the two states, but the instant one party makes a measurement, it's guaranteed that the pair particle will be measured in the other state, even if information communicating this couldn't possibly have travelled between the two in time. So far, so good.

However. Let's say you measure one of your particles. You get spin down. Then you measure another one of your particles. You get spin down as well. So what? Has Bob measured one or both of those particles? You don't know. When you send a classical, speed-of-light-constrained message to Bob, you can find out which ones he's measured and that for the ones he's measured, he's measured the other state to you as expected. But no information has been exchanged until you do that. You don't have any ability to affect the measurements made by the other party without exchanging classical information; all that happens is that the two sets of measurements, when compared, will be found to match.

What about if you prearrange who is going to measure what and when before Bob gets on the spaceship or whatever.
Isn't the uncertainty that prohibits the FTL communication then removed?
I understand that keep track of time and maintaining precise coordination in different reference frames might be tricky but achievable, no?

[red assassin]

What about if you prearrange who is going to measure what and when before Bob gets on the spaceship or whatever.
Isn't the uncertainty that prohibits the FTL communication then removed?
I understand that keep track of time and maintaining precise coordination in different reference frames might be tricky but achievable, no?

It doesn't matter, because whether or not Bob has made his measurements doesn't change anything about what Alice measures, and nothing Bob can do will change what Alice measures. Alice will measure a series of random values. Nothing Bob does changes that, so no information is transmitted.

[Bishop149]

It doesn't matter, because whether or not Bob has made his measurements doesn't change anything about what Alice measures, and nothing Bob can do will change what Alice measures. Alice will measure a series of random values. Nothing Bob does changes that, so no information is transmitted.

Ah yes, ok.
I didn't get it at first and was writing an example to you to illustrate why.
My example doesn't work. . . . I proved your point to myself. Excellent, thank you!