Can Entanglement Survive the Destruction of One Particle?

[Honorable_Death]

i was just wondering, if you have two entangled particles and one of them is destroyed, does the entanglement also get destroyed, and would anything else happen?

 

[tabasco]

Whenever you "destroy" a particle, you alway end up with a different particle or photons or whatever. All information that was carried by the particle will be coded in some form in the new particles you get. It is impossible to comletely destroy even just one bit of information without that information dissipating somewhere. The remaining particle will still be entangled with wathever is now carrying the information of the destroyed particle.

 

[vanesch]

i was just wondering, if you have two entangled particles and one of them is destroyed, does the entanglement also get destroyed, and would anything else happen?

In normal circumstances, there's no way to "destroy" a particle. You can have it "interact" with something else (say, an anti-particle) but that will always result in yet other particles coming out, depending on the state of the incoming (to be destroyed) particle, and as such, the "entanglement" lives on. There is big discussion of whether this is also true for a black hole.
Is, or isn't, a particle destroyed when it falls into a black hole ?
Of course that's a difficult question to answer. Classically, in GR, one would be tempted to say that it is... except for one detail. If the black hole is embedded in a minkowki background (meaning, far away from the black hole, spacetime is "flat"), then, for an observer far away, it takes eternity for him to see the particle fall into the black hole. If the black hole now evaporates in a finite amount of time (for the remote observer) then maybe the information got out before even disappearing.
As long as one doesn't have a decent unification of GR and quantum theory, the question will remain open, I suppose.

 

[wywong]

Whenever you "destroy" a particle, you alway end up with a different particle or photons or whatever. All information that was carried by the particle will be coded in some form in the new particles you get. It is impossible to comletely destroy even just one bit of information without that information dissipating somewhere.

Sorry I really get confused. According to information theory, entropy is loss of information. If loss of information is impossible, how comes the second law of thermodynamics?

The remaining particle will still be entangled with wathever is now carrying the information of the destroyed particle.

Suppose one of two entangled photons is absorbed by an electron, which subsequently emits a photon of the same wavelength. Can I expect the new photon to be entangled with the other un-destroyed photon? I thought aborption and re-emission cause quantum decoherence and loss of entanglement.

Wai Wong (QM newbie)

 

[Honorable_Death]

In normal circumstances, there's no way to "destroy" a particle. You can have it "interact" with something else (say, an anti-particle) but that will always result in yet other particles coming out, depending on the state of the incoming (to be destroyed) particle, and as such, the "entanglement" lives on. There is big discussion of whether this is also true for a black hole.
Is, or isn't, a particle destroyed when it falls into a black hole ?
Of course that's a difficult question to answer. Classically, in GR, one would be tempted to say that it is... except for one detail. If the black hole is embedded in a minkowki background (meaning, far away from the black hole, spacetime is "flat"), then, for an observer far away, it takes eternity for him to see the particle fall into the black hole. If the black hole now evaporates in a finite amount of time (for the remote observer) then maybe the information got out before even disappearing.
As long as one doesn't have a decent unification of GR and quantum theory, the question will remain open, I suppose.

But when a particle interacts with a anti-particle they get Annihilated and turn into energy, that would destroy the particle wouldn't it?

 

[jtbell]

But when a particle interacts with a anti-particle they get Annihilated and turn into energy,

The annihilation produces photons (particles!) which have energy.

 

[ikkyu]

Sorry I really get confused. According to information theory, entropy is loss of information. If loss of information is impossible, how comes the second law of thermodynamics?

Suppose one of two entangled photons is absorbed by an electron, which subsequently emits a photon of the same wavelength. Can I expect the new photon to be entangled with the other un-destroyed photon? I thought aborption and re-emission cause quantum decoherence and loss of entanglement.

Wai Wong (QM newbie)

Entropy is the amount of information.
It is approximately the least number of bits need to code the information.

highly ordered system ~ highly redundant data ~ low entropy
highly disordered system ~ low redundant data ~ high entropy

 

[Demystifier]

In normal circumstances, there's no way to "destroy" a particle. You can have it "interact" with something else (say, an anti-particle) but that will always result in yet other particles coming out, depending on the state of the incoming (to be destroyed) particle, and as such, the "entanglement" lives on. There is big discussion of whether this is also true for a black hole.
Is, or isn't, a particle destroyed when it falls into a black hole ?
Of course that's a difficult question to answer. Classically, in GR, one would be tempted to say that it is... except for one detail. If the black hole is embedded in a minkowki background (meaning, far away from the black hole, spacetime is "flat"), then, for an observer far away, it takes eternity for him to see the particle fall into the black hole. If the black hole now evaporates in a finite amount of time (for the remote observer) then maybe the information got out before even disappearing.
As long as one doesn't have a decent unification of GR and quantum theory, the question will remain open, I suppose.

Since you agree with me that past, presence and future equally exist from the spacetime point of view (we had a discussion about that a long time ago), you might like this:
http://xxx.lanl.gov/abs/0905.0538
Essentially, even if the particle is destroyed at the singularity in the black hole, the information is not destroyed because the full wave function of the universe describes the correlations of outgoing Hawking particles in the future with ingoing Hawking particles in the past.

 

[Pio2001]

All information that was carried by the particle will be coded in some form in the new particles you get. It is impossible to comletely destroy even just one bit of information without that information dissipating somewhere.

Let's say that we run an experiment with two EPR photons. We remove the polarizer on one side of the experiment, and let the photon run into the photomultiplicator. It ejects an electron from an atom, that in turn hits an electrode, that triggers the PM response.

Does it mean that the photon's polarization information has been scattered in the environment by means of the electron ?

Then this information, first entangled, quickly decoheres under the influence of the environment, with which it strongly interacts, exactly as if a polarization measurment had been performed.

The other photon therefore gains a defined, but, for all practical purposes, unknown, polarization.