Sufficiently advanced cryptography

 quantum contextuality has been investigated as a source of quantum advantage and computational speedups in quantum computing.

Magic state distillation

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Magic state distillation is a scheme for quantum computing in which quantum circuits constructed only of Clifford operators, which by themselves are fault-tolerant but efficiently classically simulable, are injected with certain "magic" states that promote the computational power to universal fault-tolerant quantum computing.^[46] In 2014, Mark Howard, et al. showed that contextuality characterizes magic states for qubits of odd prime dimension and for qubits with real wavefunctions.^[47] Extensions to the qubit case have been investigated by Juani Bermejo Vega et al.^[43] This line of research builds on earlier work by Ernesto Galvão,^[42] which showed that Wigner function negativity is necessary for a state to be "magic"; it later emerged that Wigner negativity and contextuality are in a sense equivalent notions of nonclassicality.

https://en.wikipedia.org/wiki/Greenberger%E2%80%93Horne%E2%80%93Zeilinger_state

the GHZ state predicts outcomes from experiments that directly contradict predictions by every classical local hidden-variable theory. The state has applications in quantum computing.