Quantum weak coin flipping with arbitrarily small bias

          @misc{ pirsa_PIRSA:08020038,
            doi = {10.48660/08020038},
            url = {https://pirsa.org/08020038},
            author = {Mochon, Carlos},
            keywords = {Quantum Information},
            language = {en},
            title = {Quantum weak coin flipping with arbitrarily small bias},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {mar},
            note = {PIRSA:08020038 see, \url{https://pirsa.org}}
          }
          

Abstract

Coin flipping by telephone (Blum \'81) is one of the most basic cryptographic tasks of two-party secure computation. In a quantum setting, it is possible to realize (weak) coin flipping with information theoretic security. Quantum coin flipping has been a longstanding open problem, and its solution uses an innovative formalism developed by Alexei Kitaev for mapping quantum games into convex optimization problems. The optimizations are carried out over duals to the cone of operator monotone functions, though the mapped problem can also be described in a very simple language that involves moving points in the plane. Time permitting, I will discuss both Kitaev\'s formalism, and the solution that leads to quantum weak coin flipping with arbitrarily small bias.