# Entagled Electrons - measuring both x and y spin

## Main Question or Discussion Point

According to QM, given two entangled electrons A and B, if you measure the y-axis spin on A to be up, then you know electron B's y-axis spin is down.

Also according to QM, if i understood it properly, you cannot then go on to measure the x-axis spin on B, because then you would know both y and x-axis spins on A, which is not allowed.

But what exactly stops you from measuring it on B?

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Nugatory
Mentor
According to QM, given two entangled electrons A and B, if you measure the y-axis spin on A to be up, then you know electron B's y-axis spin is down.

Also according to QM, if i understood it properly, you cannot then go on to measure the x-axis spin on B, because then you would know both y and x-axis spins on A, which is not allowed.

But what exactly stops you from measuring it on B?
That's not how it works; nothing stops you from making both measurements.

However, when you measure the y-axis spin of A to be up, that doesn't tell you that B's y-axis spin is down. It tells you that if you had measured B's y-axis spin it would have been down - but you didn't, you measured its x-axis spin instead. After that measurement, you'll know whether B is in the x-up or x-down state, but in either of those states a subsequent measurement of the y-axis spin will be completely random.

That's not how it works; nothing stops you from making both measurements.

However, when you measure the y-axis spin of A to be up, that doesn't tell you that B's y-axis spin is down. It tells you that if you had measured B's y-axis spin it would have been down - but you didn't, you measured its x-axis spin instead. After that measurement, you'll know whether B is in the x-up or x-down state, but in either of those states a subsequent measurement of the y-axis spin will be completely random.
Thanks for the answer, but unfortunately this seems to open even more questions.

So you say that if A measures spin up on the y-axis, and B does not measure the spin on the y-axis at all, but goes on to measure the spin on the the x-axis, the y-axis spin is back to random.
What about the y-axis spin on A. Is it back to random as well?

If B measuring the spin on the x-axis would also put A's y-spin back to random, then couldn't Bob transfer information to Alice?

For example, if Bob flipped a coin, and every time the coin turns out tail, he would measure the x-axis spin in order to "reset" Alice's electron A's spin of the y-axis, then Alice could do the measurement again on A's spin on the y-axis. If she found the spin changed, she would know Bob's coin ended up tails. If the spin remained the same, she would not know either. So 50% of the times information would pass.

Or is it the case that when Alice repeats the measurement, the result is random each time (50% chance for either up or down)?
edit: Meaning the case where Alice measures A's y-axis spin, and doing a second measurement right after before Bob measures anything at all. So if the first time A turns out to be spin up on the y-axis, on the second time it could end up to be spin down?

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Supposed re-examining the spin by Alice would potentially change the spin as outlined above, independent on if Bob measures anything or not, then couldn't Alice do any experiment that checks if her electron behaves according to how up-spin on the y-axis electrons behave, supposed she measured an up-spin initially, and then conclude that if her electron does not pass the test, Bob must have measured the x-axis or z-axis spin and therefore reset the y-spin on her electron(50% of the times)?

Nugatory
Mentor
Thanks for the answer, but unfortunately this seems to open even more questions.

So you say that if A measures spin up on the y-axis, and B does not measure the spin on the y-axis at all, but goes on to measure the spin on the the x-axis, the y-axis spin is back to random.
What about the y-axis spin on A. Is it back to random as well?
no. You get one measurement on each side, and then they're no longer entangled.

• 1 person
no. You get one measurement on each side, and then they're no longer entangled.
Straight and to the point. Thanks for the precise answer.

But it seems a bit strange how nature handles things. It does not break on the first measurement, independent on if Alice or Bob does it, but it does break on the second, like if nature would be counting the times a measurement happened, or is there some deeper reason why it breaks on the second measurement but not the first?

Nugatory
Mentor
Straight and to the point. Thanks for the precise answer.

But it seems a bit strange how nature handles things. It does not break on the first measurement, independent on if Alice or Bob does it, but it does break on the second, like if nature would be counting the times a measurement happened, or is there some deeper reason why it breaks on the second measurement but not the first?
An easy explanation using a collapse interpretation: the system of two particles started in a superposition of "A up, B down" and "B up, A down". Any measurement collapses the wave function of the system into one of those two states; and then we just have two particles that can evolve independently.

An easy explanation using a collapse interpretation: the system of two particles started in a superposition of "A up, B down" and "B up, A down". Any measurement collapses the wave function of the system into one of those two states; and then we just have two particles that can evolve independently.
Does that mean the entanglement already broke on the first measurement?

Staff Emeritus
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This is getting off the track.

If two electrons are in a spin-0 state, "entanglement" means <Sx1> = -<Sx2>
<Sy1> = -<Sy2> and <Sz1> = -<Sz2>. This says nothing about the relationship between different components of different particles: like the x-component of Electron 1 and the z-component of Electron 2.

This is getting off the track.

If two electrons are in a spin-0 state, "entanglement" means <Sx1> = -<Sx2>
<Sy1> = -<Sy2> and <Sz1> = -<Sz2>. This says nothing about the relationship between different components of different particles: like the x-component of Electron 1 and the z-component of Electron 2.
I understood entanglement to mean more than just that. Simply because two particles have opposite spin, does not make those particles entangled.

If a pair of electrons are entangled it means that the measurement on one particle's spin in either axis would effect the spin(same axis) of the particle it is entangled with.

Maybe i did not get this right however...

What i am trying to understand is, if above is the case, WHEN the entanglement breaks. It seems to me it would break right after the first measurement, OR if not, what kind of experiment would show they are entangled still after the first measurement but not after the second?

Above in this thread i understood it was one measurement on each particle which breaks it, but later down it seems it is the first measurement that would break the wave function and result in the particles having opposing spins... from which point i don't see which experiment would show they are entangled still, should this be the case.

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Nugatory
Mentor
Does that mean the entanglement already broke on the first measurement?
If you're thinking in terms of a collapse interpretation, yes.

But that comes out of the collapse interpretation, not anything that we could actually measure. It's even possible to set up the experiment in such a way that Bob's measurement is "first" for some observers but (thanks to relativity of simultaneity) Alice's measurement is "first" for other observers.

The only thing that you can take to the bank is that the first measurement of each particle will be correlated with the first measurement of the other particle according to the laws of quantum mechanics: Perfect anti-correlation if the two measurements are taken along the same axis, otherwise anti-correlated by $cos^2\theta$ where $\theta$ is the angle between the two measurements. Subsequent measurements of either particle will be consistent with their independent evolution from there.

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DrChinese
Gold Member
What i am trying to understand is, if above is the case, WHEN the entanglement breaks. It seems to me it would break right after the first measurement, OR if not, what kind of experiment would show they are entangled still after the first measurement but not after the second?

Above in this thread i understood it was one measurement on each particle which breaks it, but later down it seems it is the first measurement that would break the wave function and result in the particles having opposing spins... from which point i don't see which experiment would show they are entangled still, should this be the case.
Keep in mind that the exact answers to "what happens and when" are not currently known. The best you can get is: "It is as if ..."

The reason is that there are a lot of experiments which point point to different things. The one thing that is known, is: If you specify a specific context (experiment), the correlations can be properly predicted and they are not in accordance with local realism. Some extreme examples:

- After a measurement occurs, you can restore the original entangled state if you perform what is called "quantum erasure".
- You can entangle objects AFTER they have been measured. (Sounds impossible, eh?)
- And you can "swap" entanglement from one object to another.

The only thing that you can take to the bank is that the first measurement of each particle will be correlated with the first measurement of the other particle according to the laws of quantum mechanics:
But then we are back to one measurement on each particle, the entangled state remaining until one measurement on each side has been made.

The experiment would go like this, Alice measures the y-axis spin on electron A and finds it to be UP. Alice knows Bob would measure spin DOWN if he decided to measure the y-axis spin on his entangled electron B.

But Bob goes on to measure the x-axis spin instead and finds it to be DOWN.

a) Which result would Alice get if she decided to measure the y-axis spin of her entangled electron A, AFTER Bob does the x-axis measurement on his electron B?
Since we cannot know both the x and y axis spin at the same time, either it "resets" back to random or the x-axis measurement by Bob already broke the entanglement and Bob measuring a spin DOWN would NOT result in Allice's entangled electron A to have a spin UP on the x-axis.

It does not seem to be an overly complicated experiment, so i would think it has been done already. What were the results?

b) this is a question concerning information transfer again, but i leave this for later when a has been answered fully.

edit: to not over-complicate this by bringing relativity in. Assume both alice and bob are at rest to each other, with synced clocks, logging the x/t events/results on a piece of paper to compare after.

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But then we are back to one measurement on each particle, the entangled state remaining until one measurement on each side has been made.

The experiment would go like this, Alice measures the y-axis spin on electron A and finds it to be UP. Alice knows Bob would measure spin DOWN if he decided to measure the y-axis spin on his entangled electron B.

But Bob goes on to measure the x-axis spin instead and finds it to be DOWN.

a) Which result would Alice get if she decided to measure the y-axis spin of her entangled electron A, AFTER Bob does the x-axis measurement on his electron B?
Since we cannot know both the x and y axis spin at the same time, either it "resets" back to random or the x-axis measurement by Bob already broke the entanglement and Bob measuring a spin DOWN would NOT result in Allice's entangled electron A to have a spin UP on the x-axis.
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I'm going to guess here, because I'm use to dealing with entanglement with regards to photons rather than electrons. I'm sure if I'm wrong someone will be quick enough to correct the record.

You can measure the spin of an electron in three axis': x, y and z. If you do, you get either +1 (up) or -1 (down) for each electron.

If Bob measures his electron in the x-axis, he gets with 1/2 probability +1 or -1 spin. This presumably collapses Alice's electron's spin in the x-axis to the opposite of Bob's. However, because Alice measure's her electron's spin in the y-axis, and it is currently in (for example -1 spin in the x-axis [meaning Bob got spin +1 in the x-axis]), then it is in a superposition of +1 and -1 spin in regards to the y-axis. So performing a measurement in the y-axis will lead the final result to be either [A=Alice, B=Bob] A(+1)B(-1), A(+1)B(+1), A(-1)B(-1) or A(-1)B(+1).

Remember, each electron is measured in a different axis, which allows for Alice to obtain +1, and Bob to obtain +1 also.

Not sure if that clarifies the issue for you or not, or whether indeed I am right at all.

I'm going to guess here, because I'm use to dealing with entanglement with regards to photons rather than electrons. I'm sure if I'm wrong someone will be quick enough to correct the record.

You can measure the spin of an electron in three axis': x, y and z. If you do, you get either +1 (up) or -1 (down) for each electron.

If Bob measures his electron in the x-axis, he gets with 1/2 probability +1 or -1 spin. This presumably collapses Alice's electron's spin in the x-axis to the opposite of Bob's. However, because Alice measure's her electron's spin in the y-axis, and it is currently in (for example -1 spin in the x-axis [meaning Bob got spin +1 in the x-axis])
I assume you meant "and it is currently in (for example -1 spin in the Y-axis [meaning Bob got spin +1 in the Y-axis])"

, then it is in a superposition of +1 and -1 spin in regards to the y-axis. So performing a measurement in the y-axis will lead the final result to be either [A=Alice, B=Bob] A(+1)B(-1), A(+1)B(+1), A(-1)B(-1) or A(-1)B(+1).

Remember, each electron is measured in a different axis, which allows for Alice to obtain +1, and Bob to obtain +1 also.

Not sure if that clarifies the issue for you or not, or whether indeed I am right at all.

So if this is the case, this leads us to question b. How can this prevent information to be transferred?

If you are right, then Bob measuring the x-axis AFTER Alice measured the y-axis, you are basically saying (if i got this right), that the y-axis spin of Alice resets to 50% for each outcome.

But then Alice could simply check for the y-axis spin again, and 50% of the times it would end up to be different from what she measured initially, giving Alice information about Bob having checked for the x-axis 50% of the times, whenever the spin turns out different from what she initially measured.

I assume you meant "and it is currently in (for example -1 spin in the Y-axis [meaning Bob got spin +1 in the Y-axis])"
Yes, sorry. Must have confused myself, but if you make the appropriate replacements, then thats my response.

So if this is the case, this leads us to question b. How can this prevent information to be transferred?

If you are right, then Bob measuring the x-axis AFTER Alice measured the y-axis, you are basically saying (if i got this right), that the y-axis spin of Alice resets to 50% for each outcome.

But then Alice could simply check for the y-axis spin again, and 50% of the times it would end up to be different from what she measured initially, giving Alice information about Bob having checked for the x-axis 50% of the times, whenever the spin turns out different from what she initially measured.
No. If she measures the y-axis spin again, she'll get exactly the same result she got when she first measured it.

No. If she measures the y-axis spin again, she'll get exactly the same result she got when she first measured it.
In that case, Bob measuring the x-axis would have no effect on the x-axis spin of Alice's electron A. Because if Bob measuring the x-axis spin of his electron B would have an effect on Alice's electron A's spin, then if as you say Alice's electron retains it's y-axis spin, we would then know both the y-axis and the x-axis spin of Alice's electron.

So you are basically saying, again, if i got this right, that the electrons are no longer entangled by the time Bob measures the electron B's x-axis spin, because if they were, the x-axis measurement would have an effect on A's electron x-axis spin.

meBigGuy
Gold Member
In a simple system where you measure the first electron and then measure the second electron, the first measurement effectively breaks the entanglement and the second electron behaves simply as an electron with spin opposite the first electron.

In reality it may be more complex than that, for example http://arxiv.org/ftp/quant-ph/papers/0404/0404011.pdf

In more complex systems you can produce entanglement swapping.

There! I think I covered all the bases pointed out the last time I tried to say that.

In that case, Bob measuring the x-axis would have no effect on the x-axis spin of Alice's electron A.
*sigh*

You haven't got it right. If that was the case, there would be no entanglement.

Because if Bob measuring the x-axis spin of his electron B would have an effect on Alice's electron A's spin, then if as you say Alice's electron retains it's y-axis spin, we would then know both the y-axis and the x-axis spin of Alice's electron.

So you are basically saying, again, if i got this right, that the electrons are no longer entangled by the time Bob measures the electron B's x-axis spin, because if they were, the x-axis measurement would have an effect on A's electron x-axis spin.
As soon as we measure the y-axis of Alice's electron, all information about the x-axis disappears. It no longer holds true that if we measure Alice's electron in the x-axis and find +1, and then measure the y-axis and get +1, then we know both x and y-spins of Alice's electron. Only one spin axis can be real; either the spin result of the x-axis, or the spin result of the y-axis.

I'm getting to the point where I'm at a loss at how to explain it any simpler. Maybe someone else might be able to give it a shot.

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*sigh*

You haven't got it right. If that was the case, there would be no entanglement.
Someone above just said the entanglement already breaks after the first measurement.

...It no longer holds true that if we measure Alice's electron in the x-axis and find +1, and then measure the y-axis and get +1, then we know both x and y-spins of Alice's electron.
nowhere ever did i say that. It seems you did not read the experiment properly, which is where all the confusion stems from.
I will try to type it out in more simple in steps.

Step 1) Alice creates an entangled electron pair. Electron A and Electron B are entangled.

Step 2) Alice sends electron B toward's Bob's lab. Electron A stays with Alice in her lab.

Step 3) Alice makes a measurement on the y-axis of electron A. The result is spin UP.

Alice now knows, Bob's electron B would turn out to be spin DOWN, _SHOULD_ Bob decide to measure the spin on the y-axis of electron B

Step 4) Bob DOES NOT measure the spin on the y-axis, but INSTEAD decides to measure the spin on the x-axis of his electron B.

Up to this point i think there are no questions.

Now if you want to keep it simple as you say, you could simply answer the following questions.

a) Are the electrons entangled still AFTER Alice measures the y-spin on the A electron in her lab?

Someone above said they are not entangled after the first measurement.
Basically saying that Alice measuring the y-axis spin to be UP on her electron A, would flip the switch on Bob's electron B to DOWN on the y-axis. The electrons are no more entangled after this.
What is your take on this? Yes or no?

In case the answer to a) is that they are not entangled anymore, we are done.

Supposed they ARE entangled still AFTER Alice measures the y-axis of electron A, we get to question b)

b) Will Bob's measurement on the x-axis of electron B (NOT y-axis Alice measured) effect the x-axis spin of Alice's electron A? Bob measures it to be UP, so Alice should get DOWN.

If this is the case, then we would know BOTH the x and y spin of Alice's electron A. This is not allowed by QM as far as i understand. Leading to question c)

c) Do we know Alice's electron A's y-axis spin still? Or did the measurement by Bob on the x-axis of his electron B have an effect on the y-axis of A's electron? Did it reset it back to random? If Alice measures the y-axis for a second time, will she get the same results?

You said yes, it remains the same as before! But then we CANNOT know the x-axis spin and Bob's measurement could not possibly have effected it.

DrChinese
Gold Member
...Now if you want to keep it simple as you say, you could simply answer the following questions.

a) Are the electrons entangled still AFTER Alice measures the y-spin on the A electron in her lab?

Someone above said they are not entangled after the first measurement.
Basically saying that Alice measuring the y-axis spin to be UP on her electron A, would flip the switch on Bob's electron B to DOWN on the y-axis. The electrons are no more entangled after this.
What is your take on this? Yes or no?

In case the answer to a) is that they are not entangled anymore, we are done.
In this case, they are NOT entangled any more on the spin basis. Therefore, further measurements of Alice and Bob will NOT lead to further correlations on the x-basis. So... we are done. 