  We introduce the quantum-house effect, a non-local phenomenon which
apparently does not require quantum discord to be present. It suffices for the
effect if neither subsystem of a bipartite system is in a pure state. This way,
the quantum-house effect completely fills the gap between trivial correlations
and quantum discord. However, we discuss why the situation is more subtle than
that, by showing that in a concrete cryptographic setting called "the
quantum-house game", the ability to produce quantum discord is in fact
necessary for the quantum-house effect to work. Then, we suggest a principle
called "quantum detachment" to characterize where quantumness in general
departs from classicality, based on the information a physical system contains
about itself. The quantum-house effect is demonstrated on SpinQ Gemini, a
2-qubit liquid-state NMR desktop quantum computer.
