Quantum dice

• Rolling a die is a quantum process admitting a Hilbert space representation.
• Rolling experiments with a single die can produce interference effects.
• Two connected dice can violate Bell’s inequality.
• Correlations need to be created by the measurement, to violate Bell’s inequality.

In a letter to Born, Einstein wrote  [42]: “Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the ‘old one.’ I, at any rate, am convinced that He does not throw dice.” In this paper we take seriously Einstein’s famous metaphor, and show that we can gain considerable insight into quantum mechanics by doing something as simple as rolling dice. More precisely, we show how to perform measurements on a single die, to create typical quantum interference effects, and how to connect (entangle) two identical dice, to maximally violate Bell’s inequality.