  It is generally believed that unconditionally secure quantum bit commitment
is impossible, due to widespread acceptance of an impossibility proof that
utilizes quantum entaglement cheating. In this paper, we delineate how the
impossibiliy proof formulation misses various types of quantum bit commitment
protocols based on two-way quantum communications. We point out some of the
gaps in the impossibility proof reasoning, and present corresponding
counterexamples. Four different types of bit commitment protocols are
constructed with several new protocol techniques. A specific Type 4 protocol is
described and proved unconditionally secure. Security analysis of a Type 1
protocol and a Type 2 protocol are also sketched. The security of Type 3
protocols is as yet open. A development of quantum statistical decision theory
and quantum games is needed to provie a complete security analysis of many such
protocols.
