Finding a direct mention of a modern day scientific theory in texts that are over 5000 years old, would be an exercise in futility.
It is the implied evidence hidden in deep symbolism that can let us assume that the ancient sages new a lot about the creation & working of the universe to a fairly accurate degree.
As per Wikipedia,
Quantum Entanglement is a physical phenomenon that occurs when
pairs or groups of particles are generated or interact in ways such
that the quantum state of each particle cannot be described
independently of the others...
Or to put in the simple terms.
Even the farthest points in the cosmos are related and respond to each
other through ‘something’
Here's what Manu Smriti has to say.
1.27 But with the minute perishable particles of the five (elements) which have been mentioned, this whole(world) is framed in due order.
This sloka in it’s core talks about the same fundamental sub-atomic elements
being the building blocks of everything in the known universe.
1.20 Among them each succeeding (element) acquires the quality of the preceding one, and whatever place (in the sequence) each of them occupies, even so many qualities it is declared to possess.
This sloka mentions that since everything is made from the same basic elements,
they also have the qualities of each other.
1.26. Moreover, in order to distinguish actions, he separated merit from demerit, and he caused the creatures to be affected by the pairs (of opposites), such as pain and pleasure.
And here is the symbolism for inherent duality in nature that quantum mechanics advocates.
Coming to the relation part...
1.50. The (various) conditions in this always terrible and constantly changing circle of births and deaths to which created beings are subject, are stated to begin with (that of) Brahman, and to end with (that of) these (just mentioned immovable creatures).
Einstein called it Ether, Particle Physics calls it Higgs Field
And Quantum Mechanics calls it Entanglement
In Hinduism it is ‘Brahman’ or ‘Consciousness’
‘Brahman’ is the force behind creation and reason behind entanglement of everything in the universe.
Reference: Manu Smriti