  Unconditionally secure bit commitment and coin flipping are known to be
impossible in the classical world. Bit commitment is known to be impossible
also in the quantum world. We introduce a related new primitive - {\em quantum
bit escrow}. In this primitive Alice commits to a bit $b$ to Bob. The
commitment is {\em binding} in the sense that if Alice is asked to reveal the
bit, Alice can not bias her commitment without having a good probability of
being detected cheating. The commitment is {\em sealing} in the sense that if
Bob learns information about the encoded bit, then if later on he is asked to
prove he was playing honestly, he is detected cheating with a good probability.
Rigorously proving the correctness of quantum cryptographic protocols has
proved to be a difficult task. We develop techniques to prove quantitative
statements about the binding and sealing properties of the quantum bit escrow
protocol.
  A related primitive we construct is a quantum biased coin flipping protocol
where no player can control the game, i.e., even an all-powerful cheating
player must lose with some constant probability, which stands in sharp contrast
to the classical world where such protocols are impossible.
