4 ms·

> 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

by 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.
- kgwgk 8y ago
  I thought you were referring to the relativity of simultaneity. I'm glad you insist on the FTL communication issue, maybe now I will be able to convince you that there is no issue at all... > 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). The answer to 2 is "no". If Alice has not performed any measurement, the N "B" particles that Bob has are not in a pure state. They are a subsystem of the N (indentical) entangled pairs formed by the N "A" particles that Alice has plus the corresponding N "B" particles that Bob has (let's call that state E). So, depending on whether Alice has done the measurement or not, what we have is (I undertstand you don't really accept this description, it's for the sake of the argument where you will try to show how this description is unacceptable): Measurement not done Pairs remain entangled The N particles held by Bob are not in a pure state (The A/B pairs are in a pure state E) Measurement done Pairs are no longer entangled The N particles held by Bob are each in one definite state P or P' or P'' or P''' (Alice knows the precise state of Bob's particles, she knows how to rotate each particle to get the state P) You say that, before any message from Alice can reach Bob, he can determine wheter or not she has performed the measurement. Can you explain how? (Hint: no, you cannot.)
  - lisper 8y ago
    > I thought you were referring to the relativity of simultaneity. Yes, I was. > I'm glad you insist on the FTL communication issue, It amounts to the same thing. > maybe now I will be able to convince you that there is no issue at all... Maybe, except that I'm not sure you're clear on what we're actually disagreeing about. > You say that, before any message from Alice can reach Bob, he can determine wheter or not she has performed the measurement. Only in a hypothetical case, not realizable in practice (probably -- see below), where Bob has chosen N/4 particles at random and those just happen to coincide with the particles that Alice measured and found to require no rotation. In that case, Bob will, on your view, observe first-order interference if Alice has measured, and not otherwise. Maybe it would help if I describe it as a detailed thought experiment. The experiment takes place in four phases. Phase 1: Alice and Bob choose a basis for a pure state P which they will use for the remaining two phases. Phase 2: Alice teleports N copies of state P to Bob using the normal protocol, including the transmission of the results of her measurements. Bob takes the N/4 particles that require no rotation and tests them to see if they produce first-order interference relative to the basis of P. I trust you and I agree that he will observe interference in this case. Phase 3: This is the part that can't be realized in practice, and I have to number the steps here because this phase runs in a loop. Phase 3 is designed to answer the question: what would have happened in phase 2 if Bob had chosen the same N/4 particles by pure chance? So... 1. N EPR pairs are distributed. 2. Alice performs her part of the teleportation protocol, but does NOT tell Bob the results of her measurements. 3. Bob selects N/4 particles at random and tests for first-order interference relative to P. (The vast majority of the time the result will be negative.) 4. Bob and Alice compare Bob's random selections in step 3 with the results of Alice's measurements in step 2. If they happen to coincide, i.e. Bob just happened to pick the correct N/4 particles that did not require rotation, the experiment halts, with the result being whatever Bob observed on the last iteration of step 3. I trust that you and I will agree that Bob will also observe interference in this case. Phase 4 (this is the interesting one): This is identical to phase 3, except that steps 2 and 3 are reversed, i.e. Bob makes his random selection and interference measurement BEFORE (in a fully relativistic sense) Alice makes her measurements. i.e.: 1. N EPR pairs are distributed. 2. Bob selects N/4 particles at random and tests for first-order interference relative to P. 3. Bob communicates to Alice that he is done. 4. AFTER Alice receives Bob's signal from step 3, she performs her side of the teleportation protocol for N copies of P. 5. They compare the results of Alice's measurements in step 4 with Bob's random choices made in step 2. If they coincide (i.e. Bob just happened to choose the correct N/4 particles that did not require rotation) the experiment concludes, with the result being whatever Bob observed on the final iteration of step 2. Otherwise, they go to step 1 and try again. On your view, the predicted result of phase 4 will be negative. So if Alice cheats and performs her measurements before receiving Bob's signal, Bob can tell. Postscript: now that I think about it, it might actually be possible to perform this experiment. A mach-zehnder interferometer can be pretty sensitive, so it might be possible to get N down low enough that the experiment could terminate in a reasonable amount of time.

by kgwgk 8y ago

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.

kgwgk 8y ago
I thought you were referring to the relativity of simultaneity. I'm glad you insist on the FTL communication issue, maybe now I will be able to convince you that there is no issue at all... > 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). The answer to 2 is "no". If Alice has not performed any measurement, the N "B" particles that Bob has are not in a pure state. They are a subsystem of the N (indentical) entangled pairs formed by the N "A" particles that Alice has plus the corresponding N "B" particles that Bob has (let's call that state E). So, depending on whether Alice has done the measurement or not, what we have is (I undertstand you don't really accept this description, it's for the sake of the argument where you will try to show how this description is unacceptable): Measurement not done Pairs remain entangled The N particles held by Bob are not in a pure state (The A/B pairs are in a pure state E) Measurement done Pairs are no longer entangled The N particles held by Bob are each in one definite state P or P' or P'' or P''' (Alice knows the precise state of Bob's particles, she knows how to rotate each particle to get the state P) You say that, before any message from Alice can reach Bob, he can determine wheter or not she has performed the measurement. Can you explain how? (Hint: no, you cannot.)
- lisper 8y ago
  > I thought you were referring to the relativity of simultaneity. Yes, I was. > I'm glad you insist on the FTL communication issue, It amounts to the same thing. > maybe now I will be able to convince you that there is no issue at all... Maybe, except that I'm not sure you're clear on what we're actually disagreeing about. > You say that, before any message from Alice can reach Bob, he can determine wheter or not she has performed the measurement. Only in a hypothetical case, not realizable in practice (probably -- see below), where Bob has chosen N/4 particles at random and those just happen to coincide with the particles that Alice measured and found to require no rotation. In that case, Bob will, on your view, observe first-order interference if Alice has measured, and not otherwise. Maybe it would help if I describe it as a detailed thought experiment. The experiment takes place in four phases. Phase 1: Alice and Bob choose a basis for a pure state P which they will use for the remaining two phases. Phase 2: Alice teleports N copies of state P to Bob using the normal protocol, including the transmission of the results of her measurements. Bob takes the N/4 particles that require no rotation and tests them to see if they produce first-order interference relative to the basis of P. I trust you and I agree that he will observe interference in this case. Phase 3: This is the part that can't be realized in practice, and I have to number the steps here because this phase runs in a loop. Phase 3 is designed to answer the question: what would have happened in phase 2 if Bob had chosen the same N/4 particles by pure chance? So... 1. N EPR pairs are distributed. 2. Alice performs her part of the teleportation protocol, but does NOT tell Bob the results of her measurements. 3. Bob selects N/4 particles at random and tests for first-order interference relative to P. (The vast majority of the time the result will be negative.) 4. Bob and Alice compare Bob's random selections in step 3 with the results of Alice's measurements in step 2. If they happen to coincide, i.e. Bob just happened to pick the correct N/4 particles that did not require rotation, the experiment halts, with the result being whatever Bob observed on the last iteration of step 3. I trust that you and I will agree that Bob will also observe interference in this case. Phase 4 (this is the interesting one): This is identical to phase 3, except that steps 2 and 3 are reversed, i.e. Bob makes his random selection and interference measurement BEFORE (in a fully relativistic sense) Alice makes her measurements. i.e.: 1. N EPR pairs are distributed. 2. Bob selects N/4 particles at random and tests for first-order interference relative to P. 3. Bob communicates to Alice that he is done. 4. AFTER Alice receives Bob's signal from step 3, she performs her side of the teleportation protocol for N copies of P. 5. They compare the results of Alice's measurements in step 4 with Bob's random choices made in step 2. If they coincide (i.e. Bob just happened to choose the correct N/4 particles that did not require rotation) the experiment concludes, with the result being whatever Bob observed on the final iteration of step 2. Otherwise, they go to step 1 and try again. On your view, the predicted result of phase 4 will be negative. So if Alice cheats and performs her measurements before receiving Bob's signal, Bob can tell. Postscript: now that I think about it, it might actually be possible to perform this experiment. A mach-zehnder interferometer can be pretty sensitive, so it might be possible to get N down low enough that the experiment could terminate in a reasonable amount of time.