3 ms·

I would argue that using the term "entanglement" to refer to the situation where "the entanglement of the system is much more apparent" or "tensor products are

I would argue that using the term "entanglement" to refer to the situation where "the entanglement of the system is much more apparent" or "tensor products are not a good approximation anymore" is completely reasonable. In contrast, when you say that "all components of a quantum system [that appears in nature] are always entangled" then this is trivially true in a technical sense, but highly misleading. To produce and stabilize non-trivial amounts of entanglement in a way that it can be harnessed for quantum information processing is certainly an interesting and highly non-trivial task which people are spending lots of effort on.

Xcelerate 12y ago
I don't think it's trivially true in a technical sense at all. It certainly didn't have to be the case that all quantum systems exhibit entanglement. Physics could have been different, such that entanglement is a property only some systems can have. And that would lead to drastically different conclusions. In fact, treating entanglement as something special is, at least for me personally, the highly misleading concept. When I was learning quantum mechanics, there were many concepts that confused and bothered me because people explained things in a loose and inaccurate way. Other incorrect statements that confused me for a long time include: "Fermions cannot occupy the same quantum state. Bosons can." "It's not possible to measure the position and momentum of a particle simultaneously." And while not QM: "Mass can be converted to energy." Essentially, schools teach the approximations first, which leads you to believe that reality works a certain way, and then you think of all sorts of situations where these rules lead to paradoxes and contradictions, and then you have to relearn everything the more accurate way, while trying to expunge the old, wrong stuff from your brain that likes to stick there. In my undergrad, I thought of plenty of ways that "entanglement", based upon the way it was explained in class could be used to transfer information faster than the speed of light. The professor didn't have a rebuke against my argument (granted this was a chemistry professor, not a physics professor), and essentially it was because everyone was repeating wrong, catchy phrases to each other. I don't think "Entanglement is the fact that a multiparticle wavefunction cannot be decomposed" is a particularly complex idea to understand. Everything else kind of falls out of that statement. In my opinion, the most accurate theory should be taught first, and then the less accurate approximations can be derived as limiting cases of the more accurate formulation. And if the math is too complex for the more accurate version, then clearly specify what fallacies or assumptions are being taken. One of my statistical mechanics books does this really, really well (the one by McQuarrie). Disclaimers are all throughout his book about how the equations apply to limiting cases and approximations, what those approximations are, and how using those approximations causes the result to differ from a more accurate theory.
- bmnmasdas 12y ago
  I guess I was being generous when interpreting your statement that "all components of a quantum system are always entangled". For pure states, such a statement is trivially true in the sense any kind of interaction in the Hamiltonian will generically create entanglement. For mixed states, your statement is of course false. It is unfortunately often the case in the real world that two subsystems are in a non-entangled quantum state. Regarding your general theme: I understand that confusion can arise if seemingly informal language is taken verbatim as a formal statement. I do not think that the solution is to abolish the former, which can be extremely efficient to reason in and communicate with (you gave some examples in your post), but rather to educate on the interpretation. It is unfortunate that this is not always done, as your experiences suggest.
  - Xcelerate 12y ago
    You have good points. However I'm going to be a little nitpicky here. Mixed states aren't exactly "real" in the sense that what is a pure state for Alice can be a mixed state for Bob (I can provide an example if you don't know what I mean). So in that case the "lack" of entanglement is simply due to ignorance of which pure state the system is actually in.
    - bmnmasdas 12y ago
      The point is that entanglement always refers to an a priori choice of subsystems (say, Alice and Bob). This is the part that makes the phenomenon non-trivial. If there are other systems around (say, Eve the environment) then the joint state of Alice and Bob will be usually be mixed as a consequence of for the "trivial" reason that we discussed in the previous posts (to adapt a famous saying, almost all components of a quantum system are always mixed ;-). There is nothing "unreal" about mixed states, and not all mixed states lack entanglement. However, for mixed states, being entangled is no longer the generic behavior. The unavoidable interactions with the environment are the reason why it is hard to maintain entanglement between subsystems. To say that we should do better and bring the environment back into the picture is missing the point if we are interested in the correlations between Alice and Bob. These do exclusively depend on their joint state (mixed or not).

Xcelerate 12y ago

I don't think it's trivially true in a technical sense at all. It certainly didn't have to be the case that all quantum systems exhibit entanglement. Physics could have been different, such that entanglement is a property only some systems can have. And that would lead to drastically different conclusions. In fact, treating entanglement as something special is, at least for me personally, the highly misleading concept. When I was learning quantum mechanics, there were many concepts that confused and bothered me because people explained things in a loose and inaccurate way. Other incorrect statements that confused me for a long time include: "Fermions cannot occupy the same quantum state. Bosons can." "It's not possible to measure the position and momentum of a particle simultaneously." And while not QM: "Mass can be converted to energy." Essentially, schools teach the approximations first, which leads you to believe that reality works a certain way, and then you think of all sorts of situations where these rules lead to paradoxes and contradictions, and then you have to relearn everything the more accurate way, while trying to expunge the old, wrong stuff from your brain that likes to stick there. In my undergrad, I thought of plenty of ways that "entanglement", based upon the way it was explained in class could be used to transfer information faster than the speed of light. The professor didn't have a rebuke against my argument (granted this was a chemistry professor, not a physics professor), and essentially it was because everyone was repeating wrong, catchy phrases to each other. I don't think "Entanglement is the fact that a multiparticle wavefunction cannot be decomposed" is a particularly complex idea to understand. Everything else kind of falls out of that statement. In my opinion, the most accurate theory should be taught first, and then the less accurate approximations can be derived as limiting cases of the more accurate formulation. And if the math is too complex for the more accurate version, then clearly specify what fallacies or assumptions are being taken. One of my statistical mechanics books does this really, really well (the one by McQuarrie). Disclaimers are all throughout his book about how the equations apply to limiting cases and approximations, what those approximations are, and how using those approximations causes the result to differ from a more accurate theory.

bmnmasdas 12y ago
I guess I was being generous when interpreting your statement that "all components of a quantum system are always entangled". For pure states, such a statement is trivially true in the sense any kind of interaction in the Hamiltonian will generically create entanglement. For mixed states, your statement is of course false. It is unfortunately often the case in the real world that two subsystems are in a non-entangled quantum state. Regarding your general theme: I understand that confusion can arise if seemingly informal language is taken verbatim as a formal statement. I do not think that the solution is to abolish the former, which can be extremely efficient to reason in and communicate with (you gave some examples in your post), but rather to educate on the interpretation. It is unfortunate that this is not always done, as your experiences suggest.
- Xcelerate 12y ago
  You have good points. However I'm going to be a little nitpicky here. Mixed states aren't exactly "real" in the sense that what is a pure state for Alice can be a mixed state for Bob (I can provide an example if you don't know what I mean). So in that case the "lack" of entanglement is simply due to ignorance of which pure state the system is actually in.
  - bmnmasdas 12y ago
    The point is that entanglement always refers to an a priori choice of subsystems (say, Alice and Bob). This is the part that makes the phenomenon non-trivial. If there are other systems around (say, Eve the environment) then the joint state of Alice and Bob will be usually be mixed as a consequence of for the "trivial" reason that we discussed in the previous posts (to adapt a famous saying, almost all components of a quantum system are always mixed ;-). There is nothing "unreal" about mixed states, and not all mixed states lack entanglement. However, for mixed states, being entangled is no longer the generic behavior. The unavoidable interactions with the environment are the reason why it is hard to maintain entanglement between subsystems. To say that we should do better and bring the environment back into the picture is missing the point if we are interested in the correlations between Alice and Bob. These do exclusively depend on their joint state (mixed or not).