I What is the limit in size that two particles/objects can be entangled?

[jaketodd]

What is the limit in size that two particles/objects can be entangled?

With the double slit experiment, I know that there are matter waves, of large size - not just individual photons.

So can a matter wave be entangled with another one, or even just a single particle with the matter wave?

Thanks.

https://en.wikipedia.org/wiki/Matter_wave

https://scholar.google.com/scholar?q=matter+wave+double+slit

https://en.wikipedia.org/wiki/Quantum_entanglement

 

[jaketodd]

https://en.wikipedia.org/wiki/Double-slit_experiment

"The largest entities for which the double-slit experiment has been performed were molecules that each comprised 2000 atoms (whose total mass was 25,000 atomic mass units)."

 

[gentzen]

What is the limit in size that two particles/objects can be entangled?

The limit is not in size, but in reachable quantum phase space (given the relevant interactions, time, and temperature).
(And it is probably not a hard limit either, but an impossibility of the sort of a control chain. A simple model of such a control chain would be that you have to try to control the value of some variable by controlling its n-th (time) derivative, when all you can observe directly is the value itself. For sufficiently big n, this is impossible in practice, despite the absence of a "biggest n" which still can be controlled in theory.)

 

[jaketodd]

The limit is not in size, but in reachable quantum phase space (given the relevant interactions, time, and temperature).
(And it is probably not a hard limit either, but an impossibility of the sort of a control chain. A simple model of such a control chain would be that you have to try to control the value of some variable by controlling its n-th (time) derivative, when all you can observe directly is the value itself. For sufficiently big n, this is impossible in practice, despite the absence of a "biggest n" which still can be controlled in theory.)

That's way over my head. Please break it down if possible. Thanks

 

[gentzen]

That's way over my head. Please break it down if possible. Thanks

If you work at very low temperature, then you can entangle very large and heavy objects. And if you work on very short time scales, then you can live with shorter decoherence times, and hence "entangle" larger and heavier objects. ... And if you work in absolute vacuum, and can suppress nearly all possible interactions, then again entangling larger and heavier objects gets possible.
(Additionally, it is hard to come-up with absolute limits for control tasks. Take some simple control example, like driving a car with a trailer backwards. And then imagine not just one trailer, but a chain of n-trailers. At some point this control task will simply overwhelm you, even if there is no fixed theoretical limit.)

 

[jaketodd]

If you work at very low temperature, then you can entangle very large and heavy objects. And if you work on very short time scales, then you can live with shorter decoherence times, and hence "entangle" larger and heavier objects. ... And if you work in absolute vacuum, and can suppress nearly all possible interactions, then again entangling larger and heavier objects gets possible.
(Additionally, it is hard to come-up with absolute limits for control tasks. Take some simple control example, like driving a car with a trailer backwards. And then imagine not just one trailer, but a chain of n-trailers. At some point this control task will simply overwhelm you, even if there is no fixed theoretical limit.)

Awesome! Thanks!