Can quantum entanglement "communicate" with its partner if one particle is in a black hole?

Title kinda says it all.

Imagine you entangled two particles then dropped one particle in a black hole.

Would changing the particle you have with you (or if something changed the particle in the BH) would the other particle get the “message”? Or is entanglement broken at the event horizon?

Missed edit window:

I know you cannot send messages this way. Just wondering if the link is broken when one particle falls into a BH.

I think this is the same question:

You have a pair of shoes - except for some reason, they’re individually boxed and unlabelled; you take one box and throw it in a black hole, then open the other box you kept. It contains the right shoe. Is the shoe in the black hole still a left shoe?

See
Black hole information paradox

There isn’t a physical link between the particles so this really isn’t a problem and as soon as one particle crosses the event horizon of the black hole they will no longer be entangled anyway.

This isn’t a good analogy for entanglement. If, at the point of emission, one particle was “left” and one was “right” inside then that would constitute a local hidden variable.
But local hidden variables have been ruled out by Bell’s inequality violations.

OK, they’re Schrodinger’s shoes.

You can’t tell from just looking at an electron whether it’s entangled or not – you need to be able to perform measurements on both entangled partners. So the electron whose partner is thrown down the black hole will act just like any other electron will.

However, doing quantum theory in the vicinity of a horizon (black hole or otherwise) does encounter some new twists which are related to entanglement across the horizon. Basically, if you ‘hide’ one part of the system behind a horizon, the whole system is not in what’s called a ‘pure state’ anymore – it is mixed (for present purpose, consider a pure state to mean a state you have maximum knowledge about, where a mixed state consequently refers to a state you don’t have maximum knowledge about). This means that it has a non-vanishing entropy, and is in fact a thermal state – this is the origin for things such as the Unruh effect and Hawking radiation.

Someone asked this same question back in September of last year. My way of thinking about it is pretty much the same as it was then.