4 ms·

Fine, but this approach leads nowhere. Before you said that “Before teleportation C is in a pure state”. But that’s surely impossible, because wherever C is com

by kgwgk 8y ago

Fine, but this approach leads nowhere. Before you said that “Before teleportation C is in a pure state”. But that’s surely impossible, because wherever C is coming from it’s entangled with a gazillion things already... If the original state C can be “pure”, then the final state B can be “pure” as well (and identical to C). I think you have a problem with the probabilistic nature of QM, if you only can accept a statistical mixture as being part of an entangled pure system. FTL signaling is just a excuse (and you don’t explain how standard QM would allow for it).

lisper 8y ago
> this approach leads nowhere. It has led to a great deal of mental clarity for me. YMMV. > Before you said that “Before teleportation C is in a pure state”. But thats surely impossible, because wherever C is coming from it’s entangled with a gazillion things already... That's right, and indeed figuring out how a laser actually works is quite challenging. http://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzle.html http://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzl... https://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzle-part-deux.html https://blog.rongarret.info/2018/05/a-quantum-mechanics-puzz... https://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzle-part-drei.html https://blog.rongarret.info/2018/05/a-quantum-mechanics-puzz... > If the original state C can be “pure”, then the final state B can be “pure” as well (and identical to C). Only if you are willing to explain how B was transformed from its initial state into its final state, and more to the point, when this transition happened. > I think you have a problem with the probabilistic nature of QM Huh? What have I said that leads you to believe that? It's not true. > if you only can accept a statistical mixture as being part of an entangled pure system That has more to do with philosophy than physics. Does an apple really fall because gravity is pulling down on it? No, but it's a good enough approximation to the truth that it's usually not worth quibbling over.
- kgwgk 8y ago
  > how B was transformed from its initial state into its final state, and more to the point, when this transition happened. There is a full description here: https://en.wikipedia.org/wiki/Quantum_teleportation#Formal_presentation https://en.wikipedia.org/wiki/Quantum_teleportation#Formal_p... It's difficult to copy formulas here but essentially A and B are in one Bell state at the beginning. When Alice makes a measurement in the basis of the Bell states for C and A, the result is that B will now be in one of the states alpha|0> + beta|1> alpha|0> - beta|1> beta|0> + alpha|1> beta|0> - alpha|1> Alice knows which one of the four is the pure state of B after the measurement and tells Bob how to rotate the state (if needed) to recover alpha|0> + beta|1> So, again, when Alice does the measurement the state becomes one of the four listed states and when Bob rotates the state (if needed) B is the same state that C was originally. Maybe you agree that this is making correct predictions of experimental results, maybe not. I still don't know when and how does B change along the procedure according to your view. > No, but it's a good enough approximation to the truth that it's usually not worth quibbling over. Talking about "pure" states after a measurement is a good enough approximation to the truth, but you find it worth quibbling over :-)
  - lisper 8y ago
    > When Alice makes a measurement in the basis of the Bell states for C and A, the result is that B will now be in one of the states... The problem with that description is that the word "now" is not well defined when Alice and Bob are far apart. > but you find it worth quibbling over Well, yeah. Just because I'm willing to accept an approximation to the truth doesn't mean I stop caring about the actual truth.
    - kgwgk 8y ago
      > The problem with that description is that the word "now" is not well defined when Alice and Bob are far apart. Do you have an alternative description to work around this "problem"? QM is a non-relativistic theory. In this case, the measurement on C/A is strictly before the rotation on B so there is not even the shadow of a problem. Relativistic extensions to QM are Lorentz-invariant and for space-separated observables there is a restriction for operators to be commuting (so the outcome is consistent with either of the observations being "first").
      - lisper 8y ago
        > Do you have an alternative description to work around this "problem"? I like this approach: https://arxiv.org/abs/quant-ph/9605002 https://arxiv.org/abs/quant-ph/9605002 > the measurement on C/A is strictly before the rotation on B so there is not even the shadow of a problem Yes, obviously. That is not what I'm talking about. Consider this variation on the theme: Alice and Bob share N>>1 entangled A-B pairs. Alice prepares N additional C particles, all in a known pure state P, and runs them all through the teleportation protocol. But instead of sending Bob rotation instructions, she sends him only the serial numbers of the particles that do not require Bob to perform a rotation. Bob keeps the particles corresponding to those serial numbers, and destroys the rest. I presume you will agree that Bob now has a collection of approximately N/4 particles in a pure state P. (I do not agree with this, BTW, but I accept it here for the sake of argument.) Now imagine that Bob simply selects N/4 particles at random without any information from Alice. He has no idea what Alice has done on her end, or indeed if she has done anything at all. There are now three cases: 1. Alice has performed her measurements, and by pure chance Bob has selected the same set of particles that Alice would have told him to select. I presume that in this case you would agree that this set of particles is still in state P. (The odds of this happening are, of course, vanishingly small, but still >0, and this is a thought experiment.) 2. Alice has NOT performed any measurements. Are Bob's particles still in state P? 3. Alice has performed measurements, and Bob's random selection does not match Alice's list of particles that don't require rotation. (This is the overwhelmingly likely scenario, of course.) In this case, Bob's particles are not in state P (because 3/4 of them require a rotation). But are they in some other pure state Q? The answer to 2 and 3 must be "yes" if you want to avoid FTL (because otherwise Bob could determine whether or not Alice has performed measurements). So the conclusion is: if you randomly select N/4 particles from a mixed population, the resulting particles are all in some pure state. Do you agree with this? If so, were those particles in that same pure state before they were selected? The conclusion I'm driving towards is that purity of state has nothing to do with the actual physical situation, it's a matter of perspective. Any physical state can appear to be pure if you look at it in the right way, but finding the "right way" to look requires additional information, i.e. information from Alice. Nothing Alice does changes anything about the physical situation on Bob's side. It simply produces the information Bob needs in order to look at his particles in the "right way" to see a particular pure state.

by kgwgk 8y ago

lisper 8y ago

> this approach leads nowhere. It has led to a great deal of mental clarity for me. YMMV. > Before you said that “Before teleportation C is in a pure state”. But thats surely impossible, because wherever C is coming from it’s entangled with a gazillion things already... That's right, and indeed figuring out how a laser actually works is quite challenging. http://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzle.html http://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzl... https://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzle-part-deux.html https://blog.rongarret.info/2018/05/a-quantum-mechanics-puzz... https://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzle-part-drei.html https://blog.rongarret.info/2018/05/a-quantum-mechanics-puzz... > If the original state C can be “pure”, then the final state B can be “pure” as well (and identical to C). Only if you are willing to explain how B was transformed from its initial state into its final state, and more to the point, when this transition happened. > I think you have a problem with the probabilistic nature of QM Huh? What have I said that leads you to believe that? It's not true. > if you only can accept a statistical mixture as being part of an entangled pure system That has more to do with philosophy than physics. Does an apple really fall because gravity is pulling down on it? No, but it's a good enough approximation to the truth that it's usually not worth quibbling over.

kgwgk 8y ago
> how B was transformed from its initial state into its final state, and more to the point, when this transition happened. There is a full description here: https://en.wikipedia.org/wiki/Quantum_teleportation#Formal_presentation https://en.wikipedia.org/wiki/Quantum_teleportation#Formal_p... It's difficult to copy formulas here but essentially A and B are in one Bell state at the beginning. When Alice makes a measurement in the basis of the Bell states for C and A, the result is that B will now be in one of the states alpha|0> + beta|1> alpha|0> - beta|1> beta|0> + alpha|1> beta|0> - alpha|1> Alice knows which one of the four is the pure state of B after the measurement and tells Bob how to rotate the state (if needed) to recover alpha|0> + beta|1> So, again, when Alice does the measurement the state becomes one of the four listed states and when Bob rotates the state (if needed) B is the same state that C was originally. Maybe you agree that this is making correct predictions of experimental results, maybe not. I still don't know when and how does B change along the procedure according to your view. > No, but it's a good enough approximation to the truth that it's usually not worth quibbling over. Talking about "pure" states after a measurement is a good enough approximation to the truth, but you find it worth quibbling over :-)
- lisper 8y ago
  > When Alice makes a measurement in the basis of the Bell states for C and A, the result is that B will now be in one of the states... The problem with that description is that the word "now" is not well defined when Alice and Bob are far apart. > but you find it worth quibbling over Well, yeah. Just because I'm willing to accept an approximation to the truth doesn't mean I stop caring about the actual truth.
  - kgwgk 8y ago
    > The problem with that description is that the word "now" is not well defined when Alice and Bob are far apart. Do you have an alternative description to work around this "problem"? QM is a non-relativistic theory. In this case, the measurement on C/A is strictly before the rotation on B so there is not even the shadow of a problem. Relativistic extensions to QM are Lorentz-invariant and for space-separated observables there is a restriction for operators to be commuting (so the outcome is consistent with either of the observations being "first").
    - lisper 8y ago
      > Do you have an alternative description to work around this "problem"? I like this approach: https://arxiv.org/abs/quant-ph/9605002 https://arxiv.org/abs/quant-ph/9605002 > the measurement on C/A is strictly before the rotation on B so there is not even the shadow of a problem Yes, obviously. That is not what I'm talking about. Consider this variation on the theme: Alice and Bob share N>>1 entangled A-B pairs. Alice prepares N additional C particles, all in a known pure state P, and runs them all through the teleportation protocol. But instead of sending Bob rotation instructions, she sends him only the serial numbers of the particles that do not require Bob to perform a rotation. Bob keeps the particles corresponding to those serial numbers, and destroys the rest. I presume you will agree that Bob now has a collection of approximately N/4 particles in a pure state P. (I do not agree with this, BTW, but I accept it here for the sake of argument.) Now imagine that Bob simply selects N/4 particles at random without any information from Alice. He has no idea what Alice has done on her end, or indeed if she has done anything at all. There are now three cases: 1. Alice has performed her measurements, and by pure chance Bob has selected the same set of particles that Alice would have told him to select. I presume that in this case you would agree that this set of particles is still in state P. (The odds of this happening are, of course, vanishingly small, but still >0, and this is a thought experiment.) 2. Alice has NOT performed any measurements. Are Bob's particles still in state P? 3. Alice has performed measurements, and Bob's random selection does not match Alice's list of particles that don't require rotation. (This is the overwhelmingly likely scenario, of course.) In this case, Bob's particles are not in state P (because 3/4 of them require a rotation). But are they in some other pure state Q? The answer to 2 and 3 must be "yes" if you want to avoid FTL (because otherwise Bob could determine whether or not Alice has performed measurements). So the conclusion is: if you randomly select N/4 particles from a mixed population, the resulting particles are all in some pure state. Do you agree with this? If so, were those particles in that same pure state before they were selected? The conclusion I'm driving towards is that purity of state has nothing to do with the actual physical situation, it's a matter of perspective. Any physical state can appear to be pure if you look at it in the right way, but finding the "right way" to look requires additional information, i.e. information from Alice. Nothing Alice does changes anything about the physical situation on Bob's side. It simply produces the information Bob needs in order to look at his particles in the "right way" to see a particular pure state.