Is entanglement severed after the first interaction?

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Main Question or Discussion Point

Do we know if entanglement between two entangled particles is completely severed after the particles interact? By interact I am generally thinking of interacting with the measurement device.

Maybe another way of asking my question:
In an EPR like experiment, if you put one of the entangled photons through two polarizers (instead of a single one) that are at different angles is it possible to determine from the result of the second polarizer whether the second polarizer had any correlation effect on the other entangled photon based on what you know the first polarizer's correlation effect should have been?

This modified EPR experiment should be something that can be mathematically described by QM. I don't know how to properly formulate it yet. Does the QM math that describe this modified EPR experiment allow you to treat the addition of the second polarizer as a separate system that can be treated independently of the part of the system that encompasses the original unmodified EPR experiment?
 

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  • #2
PeterDonis
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Do we know if entanglement between two entangled particles is completely severed after the particles interact?
This is interpretation dependent.

In a collapse interpretation, once one of a pair of entangled particle has been measured, the measurement collapses the entire wave function and severs the entanglement: both particles now have definite individual states.

In a no collapse interpretation, such as the MWI, measurement just entangles the measuring device with the system being measured, so entanglement never goes away, it just spreads to include more and more things as time goes on.
 
  • #3
phinds
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In a no collapse interpretation, such as the MWI, measurement just entangles the measuring device with the system being measured, so entanglement never goes away, it just spreads to include more and more things as time goes on.
That's very interesting Peter. It seems perfectly obvious now you say it and I assume that it becomes obvious pretty early on for one who actually studies QM and the interpretations, but I am not one such and it had not occurred to me. My immediate answer to the OP was to say that of course interaction severs entanglement but since I don't really know what I'm talking about I decided I'd best keep my mouth shut (hard to do for me) and you've made it clear what a wise course that was :smile:

I know that a lot of the questions you spend time answering here on PF are very basic to you and I would like to tell you once again that I very much appreciate the time you spend enlightening us amateurs.
 
  • #4
PeterDonis
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It seems perfectly obvious now you say it and I assume that it becomes obvious pretty early on for one who actually studies QM and the interpretations
I have actually not seen this point emphasized very much in the QM literature. Perhaps it should be.

I know that a lot of the questions you spend time answering here on PF are very basic to you and I would like to tell you once again that I very much appreciate the time you spend enlightening us amateurs.
Thanks for the kudos! :smile:
 
  • #5
zonde
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In an EPR like experiment, if you put one of the entangled photons through two polarizers (instead of a single one) that are at different angles is it possible to determine from the result of the second polarizer whether the second polarizer had any correlation effect on the other entangled photon based on what you know the first polarizer's correlation effect should have been?
Theoretically if you replace polarizer with polarization beam splitter (PBS) you can mix outputs of PBS back together and restore entanglement. But then you can know nothing about the first measurement and it does not matter.
Otherwise there shouldn't be any effect of the second polarizer on the measurement of the other photon as there is no interference in the second measurement.
 
  • #6
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Theoretically if you replace polarizer with polarization beam splitter (PBS) you can mix outputs of PBS back together and restore entanglement. But then you can know nothing about the first measurement and it does not matter.
I'm not sure if that is true. If an entangled photon is projected in a polarizer and the entanglement ends, that increases entropy which is non-unitary (loses coherence) and there cannot be recombination.
Otherwise there shouldn't be any effect of the second polarizer on the measurement of the other photon as there is no interference in the second measurement.
Because there on longer any correlation ?
 
  • #7
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Some may say that the entanglement now applies to the measuring apparatus'
 
  • #8
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Some may say that the entanglement now applies to the measuring apparatus'
If that is directed to me, I did say 'if the entanglement ends' to avoid that objection ...
 
  • #9
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If that is directed to me, I did say 'if the entanglement ends' to avoid that objection ...
No, just a remark by itself.
 
  • #10
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There is no first interaction. The interactions are spacelike separated, so they are always simultaneous in some frame.
 
  • #11
DarMM
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In a no collapse interpretation, such as the MWI, measurement just entangles the measuring device with the system being measured, so entanglement never goes away, it just spreads to include more and more things as time goes on.
Note that what exactly "the measuring device becomes entangled with the system and the environment" means is also interpretation dependent. In Many-Worlds it of course implies the device enters into a superposition of states. In some other interpretations it just means the system, environment and the device are correlated.

The interpretation neutral way of saying it would be the device, the environment and the system become correlated in a way that cannot be understood as ignorance of their individual states evolving under local physical laws. Decoherence then tells us that for the system and device alone they become correlated in a way that is for all practical purposes the same as ignorance of their individual states.

(I know you know this PeterDonis, just thought others might not)
 
  • #12
PeterDonis
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what exactly "the measuring device becomes entangled with the system and the environment" means is also interpretation dependent
This is not true as regards the math; the math is unambiguous about what this means.

What is interpretation dependent is whether the entangled state that the math gives you is the actual state of everything (the measured system plus the measuring device plus the environment), as in the MWI, or collapses to one of its branches, as in collapse interpretations. But the collapsed state is no longer entangled, at least not with respect to the measured system and the measuring apparatus (the environment can still be entangled with other things).
 
  • #13
DarMM
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This is not true as regards the math; the math is unambiguous about what this means.
By the unambiguous statement of the math, do you mean "that they are correlated in the following manner"? I would still think the physical meaning of that correlation is different in the different interpretations. Sorry, I'm not sure of the difference between what I'm saying and what you're saying.

(I think I'm bad at these interpretation discussions!)
 
  • #14
PeterDonis
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By the unambiguous statement of the math, do you mean "that they are correlated in the following manner"?
No, I mean the state vector in the Hilbert space of measured system system + measuring device + environment that is entangled (i.e., it cannot be written as a product of states of the individual subsystems). That's what the math, more precisely the Schrodinger Equation, tells you you get when the measuring device interacts with the measured system and then with the environment.
 
  • #15
DarMM
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No, I mean the state vector in the Hilbert space of measured system system + measuring device + environment that is entangled (i.e., it cannot be written as a product of states of the individual subsystems). That's what the math tells you you get when the measuring device interacts with the measured system and then with the environment.
Okay, but I'm not really disagreeing with that anywhere, I'd have to disagree with the Hilbert Space formalism to disagree with that.

I'm just saying what that entanglement means is interpretation dependent, as I think intro text books don't tend to emphasise the Epistemic view too much.
 
  • #16
PeterDonis
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I'm just saying what that entanglement means is interpretation dependent
And I'm saying it isn't. What entanglement means is that the state vector in the Hilbert space can't be written as a product of states of subsystems. That's what it means. If you want a more "physical" way to say it, "entangled" means none of the subsystems have a definite state at all; only the complete system composed of all of the subsystems does.

What interpretations differ on, as I said, is whether the entangled state that the Schrodinger Equation tells you you get when a measuring device interacts with a measured system (and then with the environment, but we don't even need to consider that part here) is the state after the measurement (as in the MWI), or whether the state collapses to one of the terms in the entangled state (as in collapse interpretations), at which point it is no longer entangled. That doesn't change the meaning of "entangled"; it changes whether the state stays the entangled state, or not.
 
  • #17
DarMM
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I see what you mean. I suppose what I'm trying to say is that even ignoring measurement in some interpretations the subsystems do have individual definite states (underlying ontic states), but they wouldn't have individual pure quantum states.

EDIT: In other words the mathematical meaning of course doesn't change between interpretations (nonproduct state on a multiparticle Hilbert Space), but the physical meaning does, i.e. whether the individual systems have definite states. This latter meaning is separate from the collapse/no-collapse distinction.
 
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  • #18
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In quantum mechanics, particles are not "things" like little marbles or waves in a lake. Attempting to think of them as such is only as useful as it allows you to gain intuition for a real experiment. Attempting to interpret particles as "things" is backwards just like ether theory was backwards. Physicists were familiar with waves in materials, so they tried to interpret electromagnetic "waves" the same way. Same issue with quantum mechanics. Instead of asking how some non quantum notion of particles can behave like that, you should be asking how that behaviour leads to the things around you. Like waves in the ether, you are trying to analogize from the top down instead of building from the bottom up.
 
  • #19
PeterDonis
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In quantum mechanics, particles are not "things" like little marbles or waves in a lake.
I don't think the OP was assuming they were. "Particles" in QM is a useful shorthand for the kinds of states that are used in EPR experiments, and I don't think the OP was putting any unusual or unwarranted interpretation on that term.
 
  • #20
DrChinese
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There is no first interaction. The interactions are spacelike separated, so they are always simultaneous in some frame.
They can be brought together again and be measured at the same location, one before the other. I would say that is objectively forcing one to occur before the other.
 
  • #21
zonde
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I'm not sure if that is true. If an entangled photon is projected in a polarizer and the entanglement ends, that increases entropy which is non-unitary (loses coherence) and there cannot be recombination.
Here is reference: J.H. Eberly, Bell inequalities and quantum mechanics (2001)
I took it from DrChinese article that is related to that prediction.
 
  • #22
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Here is reference: J.H. Eberly, Bell inequalities and quantum mechanics (2001)
I took it from DrChinese article that is related to that prediction.
Thanks. I got the Schneider article but Eberly is not accessible.
 
  • #23
zonde
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but Eberly is not accessible.
I have no alternative to offer you. I believe I learned about that prediction from DrChinese. I have not looked for more direct source because I do not really see how it could be otherwise.
 
  • #24
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I have no alternative to offer you. I believe I learned about that prediction from DrChinese. I have not looked for more direct source because I do not really see how it could be otherwise.
I'll try to understand the DrChinese paper and work out some numbers.
Thanks.
 
  • #25
DrChinese
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