There is currently no scientific evidence or theoretical framework that supports the notion of using quantum entangled black holes, based on atoms and ions or otherwise, as a means of constructing a time machine.
Time travel, especially backward time travel, remains a highly speculative topic within physics. While there are various concepts and theories in theoretical physics that explore the possibility of time travel, such as wormholes or certain solutions in general relativity, they are largely considered to be highly hypothetical and speculative.
It's important to note that the concept of a time machine involves significant challenges and paradoxes, such as the grandfather paradox or the violation of causality. These challenges make the practical realization of time travel highly unlikely based on our current understanding of physics.
While quantum entanglement is a fascinating phenomenon, its potential for time travel has not been established. Quantum entanglement primarily describes the correlations between quantum particles, and its effects are currently understood to be limited to the realm of quantum mechanics.
It's always important to critically evaluate claims related to speculative or fringe scientific concepts, as they often exceed the boundaries of our current scientific knowledge.