  Quantum information processing shows advantages in many tasks, including
quantum communication and computation, comparing to its classical counterpart.
The essence of quantum processing lies on the fundamental difference between
classical and quantum states. For a physical system, the coherent superposition
on a computational basis is different from the statistical mixture of states in
the same basis. Such coherent superposition endows the possibility of
generating true random numbers, realizing parallel computing, and other
classically impossible tasks such as quantum Bernoulli factory. Considering a
system that consists of multiple parts, the coherent superposition that exists
nonlocally on different systems is called entanglement. By properly
manipulating entanglement, it is possible to realize computation and simulation
tasks that are intractable with classical means. Investigating quantumness,
coherent superposition, and entanglement can shed light on the original of
quantum advantages and lead to the design of new quantum protocols.
  This thesis mainly focuses on the interplay between quantumness and two
information tasks, randomness generation and selftesting quantum information
processing. We discuss how quantumness can be used to generate randomness and
show that randomness can in turn be used to quantify quantumness. In addition,
we introduce the Bernoulli factory problem and present the quantum advantage
with only coherence in both theory and experiment. Furthermore, we show a
method to witness entanglement that is independent of the realization of the
measurement. We also investigate randomness requirements in selftesting tasks
and propose a random number generation scheme that is independent of the
randomness source.
