# Quantum entanglement and information

1. Jan 10, 2009

### SW VandeCarr

It is said that quantum entanglement cannot transmit information between two points faster than light because the observed states are random. Assuming classical information theory, it's clear that if I measure photon A as 'up', than its entangled partner B must be in state 'down'. A prediction that is certain to occur carries zero (Shannon) information. However, if we consider the analogy of a coin toss: 'up' here, 'down' there, I win; "down" here, "up" there, you win; it seems we are both informed of the outcome at precisely the same instant. If I'm the first to measure the quantum state here, its seems analogous to a coin toss here, the outcome of which you are instantly informed there.

2. Jan 10, 2009

### tim_lou

but then when you get a "win", how do you know the other measurer got a "loss"? He could've just changed his mind and decided not to measure anything. There is no way you can know for sure that the other measurer actually measured something until you got a confirmation.

The "information" that you speak of is like:
1. I ask my friend to turn on his computer 10 years later. My friend promised that he will turn on his computer.
2. I travel to the other end of the galaxy for 10 years then think to myself... Yeah my friend must've turned on his computer.

Do I really gain information? no.

3. Jan 11, 2009

### debra

I could look at my cat and see that its a dead cat, and then I would know that the other person has a live cat. Well, its not information, but its something isn't it?

4. Jan 11, 2009

### DrChinese

Do we need to send you a sympathy card?

Not really sure what that something is. You can say "wavefunction collapse is instantaneous" but we really don't know for a fact that anything "physical" is occurring... much less whether it is FTL.

5. Jan 11, 2009

### debra

Yes, thanks Dr C, I then get a card from my pal - kind sympathy for my dead cat. I write back - that's amazing how did you know? She would write back saying she knew my cat was dead because hers is alive. I suppose that 'something' is knowledge not information.
But I am getting myself confused now.

6. Jan 11, 2009

### SW VandeCarr

Thanks for the responses debra, DrChinese and Tim_ Lou. I can't answer the question myself, but it seems that some kind of knowledge can be communicated outside of the light cone of a given event. Its not classical information if the correlation is unity since there are just two states and if one is 'up' the other must be 'down'. The Shannon information value for an event that is certain to occur (p=1) is zero, so its not classical information (nor do I believe it's quantum information).

However, if a random event is consequential, than real knowledge seems to be available non-locally. QM predicts, indeed depends on, non-locality. To protect Einstein's law regarding signals and lightspeed, randomness is invoked as the safeguard. Random events do not, it is said, carry information. In this case A "tosses" a quantum coin by actualizing the state of the A photon. The complimentary state of the B photon is immediately available to B (regardless of whether B chooses to look or not). By observing complimentary state, B can immediately know if she has won or lost the bet. What does this mean? Can we have non-local transfer of knowledge?

The argument that a local connection is required for A and B to agree on just what "heads" and "tails" is doesn't, in my view, change the situation. Clearly this agreement must be communicated across a time-like interval in the past, but this does not preclude some kind meaningful communication across a space-like interval later.

7. Jan 11, 2009

### tim_lou

I focus on the points made here again, if you get an "up" spin, the only thing you know is that the other person, if they make a measurement, will get a "down" spin.

The "if" is important here. You don't know whether he/she will measure it, all you know is that his/her measurement must yield down. This is no more different than knowing if the earth explodes, i'll die right now.

The thing is, you cannot control what spin you get (you can't control the other person's measurement either), you either get up or down and you wouldn't even know who measures the state first, if the other measurer actually measures it, or if the measurer is alive. You have no information about what's going on on the other side. All you have is a "if" this happens, you can make a prediction. The "information" you speak of is simply correlation. You can only confirm such correlation after both measures have a meeting and compare their results. In fact, you can't even be sure if the particle was entangled until you have this meeting.

Also, thinking of relativity, you could boost to a frame where measurer A performs the experiment first and then to another frame where measurer B performs the experiment first. The quantum mechanical explanation is the same. You could say measurer B forces measurer A's result, or measurer A forces measurer B's result, either way is consistent with QM and relativity. Relativity says that causality must not be violated, and indeed in this situation, both explanations yield the same result (either A causes B or B causes A).

Last edited: Jan 11, 2009
8. Jan 11, 2009

### Autochthon

So is it meaningful to ask -- if there is a 3rd party that exists outside the light cones of both A and B but inside the the light cone of the entangled pair It can make an observation with no effect on the correlation of A and B?

9. Jan 12, 2009

### debra

The correlations works instantly regardless of light cones.

10. Jan 12, 2009

### SW VandeCarr

There have been a number of experiments using "delayed" choice within the confines of a laboratory setting. Consider a thought experiment where A is on Earth and B is on Mars at a time when the distance between is about 10 light minutes. All the details of the experiment have been agreed to before, when B was on Earth. An entangled photon pair is emitted from a satellite between Earth and Mars, directed to detectors on Earth and Mars. B's actions will be time coordinated with A's based on relativistic corrections for the signal delay and the different velocities of Mars and Earth. If the satellite is closer to Earth, A will have determined the state of photon A and photon B before photon B reaches B. Once photon B registers in the detector on Mars, B will observe the result and know if she has won or lost. Clearly, in well conducted experiment, B can know the result while still outside the light cone of A.

The issue has nothing to do with how B actually behaves. What's critical is that B CAN know the outcome non locally. Random outcomes can be assigned meaning locally prior to the experiment. Once a random value or sequence of values is assigned meaning, it can be informative.

11. Jan 12, 2009

### Hurkyl

Staff Emeritus
None of the above has talked about transmission of information. If Alice has a bit of information she wants to send to Bob, she cannot use any of these experiments as a channel for sending that information.

That locality is respected here is evident in the algebra. If we consider as observables only the things Bob can determine by experiment, that amounts to taking a partial trace of the state space: the totality of the quantum state accessible to Bob is entirely described by "the spin of my photon is in a totally mixed state". As such, it cannot be affected by any action of Alice.

Note that even if we adopt a collapse interpretation of quantum mechancs, the math does not change in the above descrption: we just have a shift in semantics. e.g. if Alice does a measurement, then Bob's mixture would be due to ignorance probabilities rather than being a total description of his particle's state.

12. Jan 12, 2009

### tim_lou

I will (yet again) repeat the points made in this thread in a different manner.

Suppose you are B, you measure up spin, what information you know about A?

Can you be certain that A actually measured? Do you even know if A is alive? All you have is an agreement and that does not count as addition information. Like I mentioned before, I can agree to turn on my computer 10 years from now while you travel to the other end of galaxy, 10 years later, you know that I have probably turned on my computer, but do you gain information? Again, I repeat, all you have is an "if", you know that if A measures the other particle, he/she will get down spin, nothing more.

Also, the argument that you make is no more different than the classical case. Suppose you have two boxes, one is empty, the other has $20,000. neither of you know which one has the $$. One of you randomly take one box, then travel to the other end of the galaxy, and open the box. So do you now gain information about the other person? 13. Jan 13, 2009 ### SW VandeCarr I have conceded in my original post that what passes between A and B is not classical information. What I am saying is that B can know whether the bet was won or lost as soon as A observes the A photon of the entangled pair and the quantum state is actualized. B will necessarily observe the state of the B photon in the complimentary state. Whatever you call it, is not B able to know something that was not known before? Tim_Lou's example of two boxes is not, in my view, analogous to this situation since it doesn't involve non-locality in any sense. 14. Jan 13, 2009 ### tim_lou I am not going to repeat my arguments here. Perhaps your definition of (useful) information is different, and all of my attempts seem to be futile. One can play with semantics all day long and talk about information travel faster than light. All of these is secondary, the crucial point is that A cannot send a message faster than the speed of light. If you claim that useful information can travel fast than light, then design an experiment that creates a signal in A and send it to B so that B receives it faster than distance/c. So, suppose A wants to send a message saying that he/she's got a down spin, what should A do? Last edited: Jan 13, 2009 15. Jan 14, 2009 ### thenewmans (Keep in mind entanglement is used for communication but only as quantum encryption. No FTL messages.) Hmm, so Dad stays on Earth and pregnant Mom goes to Mars. She doesn’t want him to have to wait 10 minutes to find out if it’s a boy or a girl after she finds out. Spin up, a boy. Spin down a girl. It’s a girl. So right away, she measures the first entangled particle. Sadly, it’s spin up. So she measures another one. This time it works. It’s spin down. Now Dad has to figure out which ones Mom measured. He assumes Mom measured the first one so he measures it. Spin down. (We expect the spins to be opposite.) But he has no way of knowing about the second one. So he still doesn’t know if it’s a boy or a girl. I guess he’ll have to wait 10 minutes. 16. Jan 14, 2009 ### DrChinese May have to wait 20 minutes if Mars is on the other side of the sun... 17. Jan 14, 2009 ### SW VandeCarr Right. So who said anything about transmitting INFORMATION about a completed event? Go back and read what I wrote: 1. Two people, to be separated by a space-like interval, agree BEFOREHAND as to the meaning and consequences of the outcome of a random process. 2. In the "quantum coin toss", say "up" wins (this is not like a real coin toss). 3. Only one of the two parties will get the "up" spin. Both parties can instantly know whether they won or loss. Last edited: Jan 14, 2009 18. Jan 14, 2009 ### tim_lou Case closed. If you are not transmitting information about a completed event, then it has nothing to do with communication faster than light. You can talk about who wins, who loses all day long but they cannot use this fact to communicate with one another. In case you want to define communication differently, the convention is that you have something and you send it to another person (i.e. a completed event). 19. Jan 15, 2009 ### SW VandeCarr Classical information is often defined by the Shannon relation: I(E) = -a log b2 P(E) where I is the information content of an event E , 'a' is a positive constant and P is probability. It's clear that if one photon of an entangled pair is spin up, the other is down with P(E)=1 and I(E)=0. No argument here. However if the spin up photon A of a correlated pair triggers a Schrodinger device which kills my cat, I can infer (non locally) that my cat is, with high probability , dead when I observe the spin down photon B (which would not trigger the device) at a space like distance. You can argue that I don't have direct information since the device could have malfunctioned, but I am moved from complete uncertainty to a higher degree of certainty. Uncertainty can be measured by the equation U(E) = 4 P (1-P) (E). U is maximal (U=1) when P=0.5 and zero when P=1 or P=0. I don't know what to call it, but it seems that one can make inferences from non-local phenomenon. Last edited: Jan 15, 2009 20. Jan 15, 2009 ### tim_lou Forget about quantum mechanics and just think about information. There are two boxes and one has$$, the other doesn't, I take one box and fly 100000000 light years away and open the box, I found it has $$in it, I can infer non-locally that the other box has no$$. If you think that this has something to do with non-local information transmission, then yeah, there is no point in arguing. If you are concerned with how this system is not truely random, then how about I find an atom, put two boxes at the two ends. Wait long enough so that it has a good chance of decaying and let each box carry a (different) particle. I immediately shield this system near perfectly so that nothing affects it until the box is opened. the point is, the information about the entangle particle is already there before you measure it. In principle, I could measure the spin of the particle right after it leaves the detector and acknowledges that my cat will die. I just choose not to measure it until I am 5 trillion light years away. This is the same thing as the classical case, where in principle, I could've known which box has$\$ before leaving earth, and none of those nonlocality question will arise. Further, there is nothing you can do to change the outcome for both cases.

Last edited: Jan 15, 2009