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My (simple) understanding of entanglement is that by measuring the spin of one entangled particle, the other entangled particles' spin changes to the opposite of measured particle. This act of measurement doesn't allow any communication. (Obviously entanglement isn't just the spin but also other physical properties, but for simplicity of this question).

However, since more than two particles can be entangled, what if a group of 3 particles are entangled, with Alice having 2 and Bob having 1.

At predetermined time intervals (eg every 0.1ms), Bob measures his entangled particle if he wishes to communicate a 1 in binary times. This will cause Alice's two entangled particles (in the same entanglement group) to have the same, opposite spin direction of Bob's particle.

Bob does not measure his entangled particle if he wishes to communicate a 0. This keep all of the 3 entangled particles still in a superposition.

At every 0.1ms, Alice measures both of her entangled particles. If Bob has already measured the entangled particle, Alice will find that both of her entangled particles have the same spin. However, if Bob has not measured, then when Alice measures one of her entangled particles, the other entangled particle will change to the opposite spin state, and Alice will find her two entangled particles are different. This would mean that information would be passable.

What's the problem with this?

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Your understanding of entanglement is wrong. The probabilities of measurement results on Alice's particles are not affected at all by any measurements performed on Bob's particle. What happens when Bob's particle is measured? The measurement apparatus differentiates into two versions, each of which has recorded one of the possible outcomes. Alice's particles become correlated with Bob's when the measurement results are compared because the decoherent systems that carry the measurement outcomes also carry locally inaccessible information. Their observables depend on what Bob has measured but the expectation values of those observables do not depend on the measurement, see

http://xxx.lanl.gov/abs/quant-ph/9906007

http://arxiv.org/abs/1109.6223.

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What's the problem with this?

The problem is that this:

My (simple) understanding of entanglement is that by measuring the spin of one entangled particle, the other entangled particles' spin changes to the opposite of measured particle.

is not true.

What is possible for example is to use 3 particles to make this state: $$\newcommand{\ketrm}[1]{\left|\mathrm{#1}\right\rangle} \newcommand{\ketThree}[3]{\ketrm{#1}\ketrm{#2}\ketrm{#3}} \frac{1}{\sqrt 2}(\ketThree{up}{down}{down} + \ketThree{down}{up}{up})$$

so that if we measure up for the first one, the two other will be down and vice versa, but it doesn't allow us to pass information.

EDIT: Ok so what you want to do is something like: $$\frac{1}{\sqrt 2}(\ketThree{up}{down}{up} + \ketThree{down}{up}{up})$$

So that if particle "a" is up, "b" and "c" are different, and if a is down, b and c are both up.

Whatever Bob does, Alice has 1/2 to measure b as down and c as up, and 1/2 to measure b and c as up.

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  • $\begingroup$ kind of figured that.. what would be a more correct understanding? $\endgroup$ – user47567 May 30 '14 at 8:57
  • $\begingroup$ @user47567 It's not really correct to say that the particle's spin changes to be the opposite of the measured particle, because neither of the particles have a definite spin before those spins are measured. It will simply happen that when the two spins are measured they will be correlated. $\endgroup$ – Jordan May 30 '14 at 9:00
  • $\begingroup$ @agemO, but that seems to let you pass information? If by measuring up for the first one, the other two will be down, then Alice would be able to derive if Bob has measured or not, by measuring both of her particles and seeing if they are the same state (Bob already measured) or see if they are different state (Bob did not measure, and Alice's first measure results in a different state). $\endgroup$ – user47567 May 30 '14 at 9:08
  • $\begingroup$ sorry no, I don't mean that -- I mean the first state. If a is measured, b and c will be the same. If b is measured, a and c will be the same, right? This should make it possible to determine if a has been measured or not. Or is it not possible to create this state? $\endgroup$ – user47567 May 30 '14 at 9:25
  • $\begingroup$ Possible state are all the linear combination, as those I have written, I don't know what you mean but none of all the possible state we can write can allow us to transmit information $\endgroup$ – agemO May 30 '14 at 9:41

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