# Finite-time disentanglement

1. Jan 6, 2016

### T S Bailey

Is there any way in which an isolated macroscopic system, through interaction with itself for a very long but finite time, could become completely disentangled with any and all external environments? I'm aware of entanglement sudden death, but it's my understanding that this is a very special case, and that we should expect entanglement to diminish asymptotically in most physical interactions. My question is whether this is theoretically possible.

2. Jan 6, 2016

### Staff: Mentor

If it's isolated it's not entangled with the external environment in the first place.

3. Jan 6, 2016

### T S Bailey

I apologize for being vague. I meant that if we have a physical system which is entangled (to whatever degree) with an environment, and then is separated from that environment for a finite time, will the degree of entanglement diminish asymptotically or will it reach zero before infinity?

4. Jan 10, 2016

### jfizzix

If the system is initially entangled with the environment, and then is placed in a situation where it can no longer interact with the environment, the entanglement will remain precisely the same (entanglement is invariant under local unitary transformations like time evolution without interaction).

Just as interaction is needed to create entanglement, interaction is also needed to destroy it.

5. Jan 10, 2016

### T S Bailey

What I'm really curious about is the way in which the entanglement diminishes when the system begins interacting with a separate environment. Should we expect an asymptotic decrease or is it theoretically possible to achieve complete disentanglement through a finite number of interactions in a finite time?

6. Jan 14, 2016

### jfizzix

You would have to specify what system you're using as "the environment", and how the interaction between the two works.

That being said, complete disentanglement in a finite time has been studied, and it known as entanglement sudden death (ESD)
http://arxiv.org/pdf/0910.1396v1.pdf