Hi all. I'm having trouble 'getting' entanglement. We were shown the EPR paradox in a lecture once, and I didn't get it. We've also been shown quantum computing, and there was something (can't remember the details) that required an understanding of entanglement, and I didn't get it. It's a little embarrassing to be at third year level and not get it.(adsbygoogle = window.adsbygoogle || []).push({});

I've been trying to figure it out by reading stuff about it. Here is one main aspect I don't understand:

http://en.wikipedia.org/wiki/EPR_paradox

I don't get why we would expect Bob to get an answer with absolute certainty when measuring x-spin. Prior to measuring Alice's z-spin, Bob's x-spin is unknown, and therefore + or - is equally likely. AFTER measuring Alice's z-spin, the same is true. So measuring Alice's z-spin has no effect on Bob's x-spin. Only on his z-spin. Suppose Alice measures the z-spin and obtains +z, so that the quantum state collapses into state I. Now, instead of measuring the z-spin as well, Bob measures the x-spin. According to quantum mechanics, when the system is in state I, Bob's x-spin measurement will have a 50% probability of producing +x and a 50% probability of -x. Furthermore, it is fundamentally impossible to predict which outcome will appear until Bob actually performs the measurement.

Here is the crux of the matter. You might imagine that, when Bob measures the x-spin of his positron, he would get an answer with absolute certainty, since prior to this he hasn't disturbed his particle at all. But, as described above, Bob's positron has a 50% probability of producing +x and a 50% probability of -x—random behaviour, not certain. Bob's positron knows that Alice's electron has been measured, and its z-spin detected, and hence B's z-spin calculated, so its x-spin is 'out of bounds'.

If the z component of both Alice and Bob's particle are determined at creation - and opposite - then when we measure Alice's z-spin, we know Bob's. If we then measure Bob's x-spin, it will have a fifty fifty chance of being + or -. The way I have stated it, does NOT imply non-locality, therefore I am misunderstanding some aspect.

Can anyone explain what I am missing?

(EDIT: I should point out that I realise that it is understood that the spins are not determined on creation, but actually at measurement, I just don't understand how this conclusion has been arrived at. ie How does the observation that the x-component of B is random suggest that it 'knows' about the measurement made on A?)

(EDIT 2: Also, I don't understand what it means that B's x-spin is "out of bounds". It says that you can measure it and it has equal probability of being measured in each state. So how is it out of bounds? If you measure A's z-spin and then B's x-spin you know the x and z spin of both particles, violating HUP, so again I am missing something.)

(yet another EDIT:

From http://en.wikipedia.org/wiki/Quantum_entanglement

Suppose I put one red and one blue marble in a black felt bag. I shake the bag around to mix them up. Blindfolded, I remove one marble and put it in another black felt back. I give one bag to Alice. If I open my bag, I have a fifty-fifty chance of getting either red or blue. If, however, I ask Alice to look in her bag and she tells me she has a blue marble, I know with 100% certainty that my marble is red. I open my bag and, indeed, it is red. Now suppose Alice is an observer for system A, and Bob is an observer for system B. If Alice makes a measurement in the eigenbasis of A, there are two possible outcomes, occurring with equal probability:[citation needed]

Alice measures 0, and the state of the system collapses to .

Alice measures 1, and the state of the system collapses to .

If the former occurs, then any subsequent measurement performed by Bob, in the same basis, will always return 1. If the latter occurs, (Alice measures 1) then Bob's measurement will return 0 with certainty. Thus, system B has been altered by Alice performing a local measurement on system A. This remains true even if the systems A and B are spatially separated. This is the foundation of the EPR paradox.

Were the marbles entangled? Has the measurement on system A altered the outcome on system B? No. The outcome is the same as in the quote, but the interpretation is different. What am I missing?

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# Entanglement question.

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