A quantum system of two entangled particles is located near a black hole, particle A is receding from and particle B is moving towards the event horizon.
When particle B is crossing the event horizon, the quantum system seems to suffer a problem of unitarity.
But the 3 following thought experiments seem to show that there is no unitarity issue for particle A:
Case 1: Shortly after the division, particle B is changing its direction and approaching again particle A. In this case, due to gravitational time dilation, particle A is a little bit younger than particle B at the moment of their encounter.
Case 2: After the division, billions of years have passed for particle A. At this moment, from the point of view of the reference frame of particle A, particle B seems to be extremely near to the event horizon. If particle B managed to escape from the event horizon and to meet particle A again, particle A would be billions of years older than particle B.
Case 3: Now we come back to the initial description, particle A is receding and particle B is going through the event horizon. The unitary evolution is persisting until the moment when B is touching the event horizon. That is an infinite amount of time for particle A and a finite time lapse for particle B, as we saw in case 1 and case 2. Once B has crossed the event horizon, from the point of view of particle B the age of particle A can no longer be defined because particle A had reached already an age near the infinity limit, and also the unitary relation between A and B has approached an infinity limit.
