How Cooper did send such a huge amount of quantum data through the watch as morse code in Interstellar? When Cooper started sending data Murph (Mackenzie Foy) was a child and when she receives the message she was older (as Jessica Chastain) than Cooper. How did she receive so much data after so much time through the watch?
The logic that was used was that he sent each piece of data, through the watch, using morse code.
The second hand in the watch became stuck and effectively continually moved between two seconds in either short or long motions, signifying the dot and dash of morse code.
Of course, sending the data would likely have taken a colossal amount of time. But in the tesseract, time was meaningless to Cooper as he had a window into every moment of time in Murph's room. As for Murph, she had a lifetime to decode and understand the data that was being transmitted.
In the light of @Napoleon Wilson's comments, I'll add that it's possible all that was sent back was the missing part of the formula*, meaning there would be much less decoding to do. This could be sent back on a repeating loop so she could solve it in her own time. This explanation probably makes more sense, as when she has her "eureka" moment in the lab, she hasn't really aged (implying she decoded the message fairly soon after discovering it). This also makes sense as we are given to believe Cooper can affect the gravity in Murph's room, suggesting she decoded the message whilst there and took her work back to NASA to complete Brand's formula*.
* I'm aware the formula was "complete". When I refer to it being incomplete, I mean that it required the data Cooper provided to solve humanity's crisis.
As seen when Murphy erases the chalk boards, she starts writing out a complex formula in its place. This formula, while mathematically complex, is simple, and condensed alphanumeric characters that can easily be sent in a Morse code message. In math, there are multiple ways to simplify an equation or figure to be readable in simple terms. A power represents multiplying a number by itself. 4^3 is shorter than 4x4x4. 5.62x10^53 reduces the number of zeros needed by alot. Scientific notation and all.