Weak coin flipping with small bias

This paper presents a quantum protocol that demonstrates that weak coin flipping with bias ≈ 0.239, less than 1/4, is possible. A bias of 1/4 was the smallest known, and followed from the strong coin flipping protocol of Ambainis in [33rd STOC, 2001] (also proposed by Spekkens and Rudolph [Phys. Rev. A 65 (2002) 012310]). Protocols with yet smaller bias ≈ 0.207 have independently been discovered by Ambainis (2001) and Spekkens and Rudolph [Phys. Rev. Lett. 89 (2002) 227901]. We also present an alternative strong coin flipping protocol with bias 1/4 with analysis simpler than that of Ambainis [33rd STOC, 2001].  2003 Elsevier B.V. All rights reserved.