Ok, so why must the universe be unreal if it is not perceived in the state of deep sleep?
Start with the advaitic definition of reality - reality is trikAla abhAdita satya - that which is never contradicted in the past, present and future. This is more or less the definition of reality.
Sruti says that in the state of deep sleep everything is contradicted -
Brihadaranyaka upanishad 4.3.22
- In this state (of deep sleep) a father is no father, a mother no mother, the worlds no worlds, the gods no gods, the Vedas no Vedas. In this state a thief is no thief, the killer of a noble Brāhmaṇa no killer, a Caṇḍāla no Caṇḍāla, a Pulkasa no Pulkasa, a monk no monk, a hermit no hermit. (This form of his) is untouched by good work and untouched by evil work, for he is then beyond all the woes of his heart (intellect).
So above Sruti statement shows that universe cannot be real, because, as we saw earlier, reality is never contradicted.
However, you raise an interesting point -
If one person is in deep sleep (who doesn't perceive the universe), there may be other persons at the same time who are awake who still perceive the same universe, and may also be interacting with each other. Doesn't that mean the universe is real?
You are correct. If X is sleeping and Y is awake, universe is contradicted only for X and not for Y. Why do we still call the universe unreal?
Let me narrate an analogy here. Two persons X and Y are independently observing a snake. The snake is actually not a real snake. They are actually looking at a rope and imagining it to be a snake. In this situation, the snake appears real for both, but we who are outside the story know that the snake is unreal.
After sometime, X comes to the realization that the snake is actually a rope. But Y is still under illusion of snake. Irrespective of what Y sees, the rope is the reality.
Now let us make the analogy more dramatic. There are 1000 people of whom person # 1 knows that the snake is actually a rope and the rest 999 people are under the illusion that it is a snake. The snake is still unreal, though perceived by 999 people.
Extend this analogy to the universe and deep sleep. Universe = snake. Ideally, rope = brahman, but in deep sleep, there is really no awareness, so let us say rope = negation of universe. Even though people in the waking state are perceiving the universe (snake), the universe is still unreal because it is not perceived by the one who is in deep sleep. Hope that helps.