Isaac Hart said:
The first question is, why do you think any of these things? What is the basis for your information? Where did you get it from? Providing that background is crucial if you want people to help you.
Isaac Hart said:
- Quantum mechanics introduces the concept of quantization. The electron’s spin can exist in discrete states.
First, only some observables are quantized. Spin is, but position and momentum of a free particle, for example, are not.
Second, "quantization" is not actually a basic concept in QM! QM was not formulated by people saying, hey, let's see what happens if we quantize things. Quantization just happened to be a
consequence of QM for certain observables under certain conditions, which for historical reasons gave its name to the entire field.
Isaac Hart said:
- Unlike classical objects, electrons can be in a superposition of states (e.g., both “spin up” and “spin down” simultaneously).
Superposition by itself doesn't mean much, since it is, in the jargon of QM, basis dependent. For example, say I have an electron whose spin state is a superposition of "spin up" and "spin down" about a certain axis. There will be some
other spin axis for which that same electron, in the same state, will
always give "spin up" on measurement. So if I choose that other spin axis, I can describe the same electron in the same state as
not being in a superposition.
The really non-classical thing QM introduces is
entanglement, which is something different from "superposition" and is not basis dependent. See further comments below.
Isaac Hart said:
- The torque affects this superposition, leading to changes in the probabilities of different spin states.
- The interaction with the magnetic field can cause Larmor precession, where the electron’s spin precesses around the field.
Under certain conditions, yes, the time evolution of an electron's spin state in a magnetic field will lead to a change in the coefficients of "spin up" and "spin down" in its state, assuming you keep your basis fixed. But that is all a mathematical abstraction unless and until you measure the electron. You can't
observe the torque "twisting" the electron the way you can in classical mechanics. Indeed, if you try to measure the electron, you will
disrupt the smooth "twisting" behavior due to the torque, and can even prevent it from happening--this is called the "quantum Zeno effect".
Isaac Hart said:
- Coherent control of this precession allows us to manipulate the electron’s spin state precisely.
More precisely: if you let the precession happen for a precisely controlled
time, you can induce a precisely controlled change in a single electron's spin state. But note, once again, that you are not
measuring the spin state. You are just letting a certain effect happen for a certain time and
predicting that it will induce a certain change in the electron's spin state. Indeed, as noted above, you
can't measure the electron's spin while you are doing this, because it will spoil the effect. So it's not the same as classical mechanics, where you can observe such things while they happen without affecting them.
Now, having said all that: none of it has
anything at all to do with entanglement or quantum teleportation. To show the existence of entanglement, or to do quantum teleportation, you have to make
measurements of spin. (You can in principle do this with electrons, but actual experiments use photons because they are much easier to deal with. Photon polarization, for this particular application, can be treated similarly to electron spin.) And notice that
nothing I said above was about entanglement at all. I was only talking about single electrons.
If you have two entangled electrons (or photons), A and B, and you use processes like the above to manipulate the state of A, you
cannot say that you are "simultaneously" manipulating the state of B. You aren't. All you are doing is manipulating the state of A. Those operations do
nothing to B. (Indeed, quantum computing experiments
rely on this fact, that if they put qubit A through a particular gate, it doesn't change anything about qubit B.) You can
measure A, and
measure B, and see from the correlations between the measurement results that they are entangled. But you cannot "instantly" affect B by anything you do to A. That's not how entanglement works.