Question about the experimental behavior of entangled particles.

[waymore]

I have been reading quite a bit about bell pairs lately and would like to know about the actual experimental behavior of them. Here is a summary of my current understanding:

Take two particles A and B entangled in such a way as the spin of each is opposite to the other, or in other words, a pair of spin-anti-correlated particles. In the following paragraphs, "Ax" refers to the spin of particle A along the x axis, which can be either up/positive/+ or down/negative/-, and so on with particle B and the other axes (y and z) of each. These "twin" particles are separated so that they can no longer directly interact.

Measuring Ax will yield either + or - with equal probability. Say for the sake of example that it is +. In my understanding, successive measurements of Ax will yield + with a probability of 100% and the next and any successive measurements of Bx will yield - with a probability of 100%, until a different axis of either particle is measured, after which these axes will return to an uncertain state.

At this point a measurement of Ay, Az, By, or Bz will yield + or - with equal probability. Say we measure By and find it to be -. Now, measuring By will always yield - and measuring Ay will always yield +, until a different axis of either particle is measured. Measuring a different axis will cause the y axes to return to an uncertain state.

The main points which I am unsure on are (a) that measuring an axis of one particle will cause that axis and that of the twin to remain the same for consecutive measurements (i.e. without measuring a different axis), (b) that measuring Ax several times and then Bx several times will not cause the measurements to change from the first of each, and (c) that measuring any axis of either particle will cause all other axes to switch back to a superposition or uncertain state, even if some of them have been measured before.

If you guys can sort this out or point me to an accurate computer simulation of Bell Pair behavior, I will be very grateful!

 

[DrChinese]

The main points which I am unsure on are (a) that measuring an axis of one particle will cause that axis and that of the twin to remain the same for consecutive measurements (i.e. without measuring a different axis), (b) that measuring Ax several times and then Bx several times will not cause the measurements to change from the first of each, and (c) that measuring any axis of either particle will cause all other axes to switch back to a superposition or uncertain state, even if some of them have been measured before.

Welcome to PhysicsForums, waymore!

I'd say you have it correct in all essentials. A certain measurement of an observable will place its conjugate into a completely uncertain state. That observable will not change its known value unless an interaction with something else invokes a change.

 

[waymore]

I'd say you have it correct in all essentials. A certain measurement of an observable will place its conjugate into a completely uncertain state. That observable will not change its known value unless an interaction with something else invokes a change.

Good, always glad to hear that I'm right ;). The problem is that I have found a way to transmit information faster than the speed of light if things are this way. Here is my method:

Two pairs of particles (A1 and B1; A2 and B2) as described in my original question are generated and one of each pair are sent to Alice and Bob. For the remainder of this post, positive/up spin is denoted as 1 and negative/down spin is denoted 0.

Alice wants to send the bit string "101" to bob.

Alice, when she first gets her particles, measures A1x. If this yields 0, she continues; if it is 1, she measures A1y and then A1x repeatedly until A1x yields 0. This way of setting a particle pair's x spin by trial and error is the heart of the communication method: if it doesn't work, nothing else does either. Alice then uses the trial-and-error method to set A2x to 0 as well.

Bob, after waiting a period of time long enough for Alice to initialize the particles, begins to measure B2x occasionally, waiting until it yields 0 (remember, after particle initialization, A*x is 0 and B*x is 1).

Alice now takes the first bit in the string she wants to send (1 in this case) and uses the trial-and-error method to set A1x to it. She then uses the trial-and-error method to set A2x to 1 so that Bob knows that *1x now holds the next bit, and starts periodically measuring A2x until it is 0.

The next time Bob measures B2x (he is doing this periodically, remember), he will see that it is now 0 and proceed to measure B1x, invert the measurement's result (which is 0), and append that to his string of received bits (which currently consists of simply “1”). He then uses the trial-and-error method to set B2x to 1 to indicate that he is ready for the next bit.

Alice, who is periodically measuring A2x, notes that it is now 0 and continues from just after the particle initialization step with the remaining bits, as does Bob. After two more trips through this cycle, Bob ends up with the bit string “101”.

Have I just broken causality, the usefulness of light cones, special relativity, the light speed limit of propagation of information, or is something not right?

 

[DrChinese]

Good, always glad to hear that I'm right ;). The problem is that I have found a way to transmit information faster than the speed of light if things are this way. Here is my method:

Two pairs of particles (A1 and B1; A2 and B2) as described in my original question are generated and one of each pair are sent to Alice and Bob. For the remainder of this post, positive/up spin is denoted as 1 and negative/down spin is denoted 0.

Alice wants to send the bit string "101" to bob.

Alice, when she first gets her particles, measures A1x. If this yields 0, she continues; if it is 1, she measures A1y and then A1x repeatedly until A1x yields 0. This way of setting a particle pair's x spin by trial and error is the heart of the communication method: if it doesn't work, nothing else does either. Alice then uses the trial-and-error method to set A2x to 0 as well.

Bob, after waiting a period of time long enough for Alice to initialize the particles, begins to measure B2x occasionally, waiting until it yields 0 (remember, after particle initialization, A*x is 0 and B*x is 1).

Alice now takes the first bit in the string she wants to send (1 in this case) and uses the trial-and-error method to set A1x to it. She then uses the trial-and-error method to set A2x to 1 so that Bob knows that *1x now holds the next bit, and starts periodically measuring A2x until it is 0.

The next time Bob measures B2x (he is doing this periodically, remember), he will see that it is now 0 and proceed to measure B1x, invert the measurement's result (which is 0), and append that to his string of received bits (which currently consists of simply “1”). He then uses the trial-and-error method to set B2x to 1 to indicate that he is ready for the next bit.

Alice, who is periodically measuring A2x, notes that it is now 0 and continues from just after the particle initialization step with the remaining bits, as does Bob. After two more trips through this cycle, Bob ends up with the bit string “101”.

Have I just broken causality, the usefulness of light cones, special relativity, the light speed limit of propagation of information, or is something not right?

They don't stay entangled AFTER the non-commuting observation is made. At least, not in that basis. Sorry if what I said implied otherwise. So after measuring X, any Y measurement means there is no more entanglement.

 

[waymore]

They don't stay entangled AFTER the non-commuting observation is made. At least, not in that basis. Sorry if what I said implied otherwise. So after measuring X, any Y measurement means there is no more entanglement.

OK, thank you for making that clear. Too bad my communication method won't work then...