Quantum dice rolling: a multi-outcome generalization of quantum coin flipping
N. Aharon, Jonathan Silman · New Journal of Physics · 2010
The problem of quantum dice rolling (DR)—a generalization of the problem of quantum coin flipping (CF) to more than two outcomes and parties—is studied in both its weak and strong variants. We prove by construction that quantum mechanics allows for (i) weak N -sided DR admitting arbitrarily small bias for any N and (ii) two-party strong N -sided DR saturating Kitaev's bound for any N . To derive (ii) we also prove by construction that quantum mechanics allows for (iii) strong imbalanced CF saturating Kitaev's bound for any degree of imbalance. Furthermore, as a corollary of (ii) we introduce a family of optimal 2 m -party strong n m -sided DR protocols for any pair m and n .