Undergrad Quantum entanglement and parallel displacement

[Strilanc]

the state of the other particle must also be changed accordingly in order to conserve the total spin.

No, the angular momentum gets transferred into the apparatus.

This doesn't decohere the spin because the apparatus is in a large decohered/mixed state, so it's not possible even in principle to determine with good fidelity whether a +1 or -1 was added to the apparatus' total angular momentum (without access to the pure state of the entire environment). As a result, the spin remains almost entirely coherent w.r.t. the experiment when rotated.

 

[Adel Makram]

No, the angular momentum gets transferred into the apparatus.

This doesn't decohere the spin because the apparatus is in a large decohered/mixed state, so it's not possible even in principle to determine with good fidelity whether a +1 or -1 was added to the apparatus' total angular momentum (without access to the pure state of the entire environment). As a result, the spin remains almost entirely coherent w.r.t. the experiment when rotated.

The angular momentum of two entangled particles get transferred into the apparatus not only the particle which enters the apparatus.

 

[Strilanc]

The angular momentum of two entangled particles get transferred into the apparatus not only the particle which enters the apparatus.

No, the transferred angular momentum only comes from the one particle.

Because the particle is in a superposition of states there's actually two opposing transfers that happen (also in superposition). Normally this would cause more entanglement, creating a GHZ state and significantly weakening the entanglement between EPR pair, but the apparatus being in a large mixed state fixes that problem.

 

[Adel Makram]

No, the transferred angular momentum only comes from the one particle.

Because the particle is in a superposition of states there's actually two opposing transfers that happen (also in superposition). Normally this would cause more entanglement, creating a GHZ state and significantly weakening the entanglement between EPR pair, but the apparatus being in a large mixed state fixes that problem.

The Stern Gerlach device or the magnetic field in our discussion also deflects the particle into two different paths which marks the state of the particle. For example, if the particle passes the device in a spin up state, it is deflected up and vice versa, so we would not expect the particle to be detected in the same straight line which it has followed before entering the field. This can be considered as partial measurement, partial because the spin state is now reduced to two values but we don`t know which one of them is the actual state until we choose which direction we have to watch the particle. So if the particle moves in x-direction in the line y=0, we expect the particle that arrive at the screen at y=y` to be spin up and at y=-y` to be spin down. The process of momentum transfer to the device is not important here, what is important is the net result. And the net result is a partial measurement, then this also applied to the entangled particle.
So rotating the spin without measuring it, is similar to say that the particle has undefined spin before entering SG device and the device rotates that spin by a definite angle but we still don`t know the direction of spin after exiting the device because we don`t know the direction before entering the device and that is set. While what happens is that SG reduces the spin from undefined value of all possible angles to only two values 180 degree apart along the direction of the device.

 

[Truecrimson]

This means an EM field with a screen is equivalent to SG device.

SG magnet changes the particle's momentum because it produces an inhomogeneous magnetic field. Constant magnetic field only rotates the spin, so the position measurement on the screen will not tell me about the spin.