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Suppose Shaniqua and Tyrone have four pairs, a, b, c, and d, of entangled particles. They take their particles and go very far apart. If Tyrone can determine whether or not a particle is still entangled, Shaniqua could observe, for example, a and c, transmitting the binary number 1010 faster than light. So, can we determine whether or not a particle is entangled? If so, why doesn't it lead to faster-than-light information transfer?

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good question. also worth checking out the no-signalling theorem to see how this comes out in the maths. –  Mark Mitchison Dec 6 '12 at 22:49
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Entanglement is just a correlation in measured properties of the subsystems (particles) expressed in a quantum way. You may only determine whether properties are correlated (or entangled) in a given, "initial" state if you repeat some measurements of the system with the same initial state many times. If you only measure two spins, for example, once, you get some result, like up-up or up-down or down-up or down-down but none of the four possibilities is more or less entangled than others. All of them may occur in entangled initial states and all of them may occur in non-entangled initial states.

Entanglement only means "predicted properties of the two subsystems are correlated, moreover correlated in a way that isn't captured by a simple classical model of correlation". Whether the predicted properties are correlated may be determined from the probability distribution(s) but to measure the probability distribution(s), you have to repeat the experiment with the same initial state many times.

More precisely, entangled states are those that can't be written as a tensor product of wave functions describing the separate subsystems. Once at least one of the entangled variables is measured, the entanglement becomes meaningless because the value of the variable is suddenly known and we're only left with some general wave function for the other, previously entangled variable which remains unknown up to the second measurement (this reduction of the dependence of the wave function is misleadingly referred to as the infamous "collapse"). And if there is only one variable, it can't be entangled.

But nothing physical is changing about the variable that hasn't been measured yet. The overall probability distribution for various outcomes $y$ remains the same after the first measurement of the (faraway) variable $x$ is performed (imagine it's a probabilistic distribution $\rho(y)=C\rho(x_\text{just measured},y)$ that is left afterwords, $C$ is such that $\int dy\,\rho(y)=1$). So no information can be transmitted by the fact that the first measurement took place.

Quite generally, quantum mechanics doesn't need any genuine (one that could transfer useful information) faster-than-light communication to guarantee things such as correlations of measurements done with entangled states. And in relativistic, local theories – especially quantum field theories and string theory – one may prove completely generally that a superluminal transfer of information is not only unnecessary for quantum mechanics to work; it is actually prohibited and impossible, by the basic laws of special relativity.

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Ah, thank you. Excellent answer. –  hombre Dec 6 '12 at 22:29
    
Nope Motl, that explanation doesn't work. The particles have to be communicating or else the properties are pre-determined. If one particle picks a state and the other particle is completely unnafected by this, then the probability function p(y) should not be a function of x as you wrote (this is assuming the states were not pre-determined, which I know very well that you believe this is true. And in fact, this is exactly what Bell showed: no theory with pre-existing properties can reproduce quantum mechanics). –  user7348 Dec 30 '12 at 1:24
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What if you have a grouping of multiple entangled particles e.g. 4 photons entangled as one. you split up the particles and spread them over space. on observation all the particles should have the same spin and after than point they should become untangled. So an observer can observe if a flag has been set at some point in the future by checking particle state.

If you have a very large number of these particles what would stop of you from periodically checking sentinel particles for an untangled state and as soon as this is witnessed engaging in bidirectional communication by selectively detangling groups of particles waiting for the next sentinel and then reading another group of particles from the origin source?

Going back to the risk of particles being randomly untangled what would prevent some application of statistical analysis and additional particles being added to the mix to allow better signal/noise quality.

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