The characteristic correlations between parts of a quantum system, which are different from correlations we normally encounter in the classical world.
If you want to describe very highly entangled states, it is very expensive to do with classical bits
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Both quantum complexity and quantum error correction, rest on a deeper underlying idea called Quantum Entanglement
The characteristic interactions / correlations among parts of a quantum system.
Essene
With Quantum Systems even if you know information about parts of the system you could be missing out on information about the whole.
There is information in the whole that you can't see looking at the parts one at a time.
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It's very difficult to describe quantum correlations / entanglement succinctly with ordinary classical information.