Unconditionally Secure Quantum Bit Commitment Expansion

It is known that a quantum bit commitment that would be secure against all attacks allowed by quantum mechanics is impossible if a standard model of communication is used. This result was a severe step back for quantum cryptography. However, this impossibility result applies only if no bit commitment exists initially between Alice and Bob. Here we consider an initial situation in which the committer, Alice, is already commited to m bits in an information theoretic sense. These information theoretic bit commitments might have been obtained using a trusted noisy channel for example. We prove that Alice can obtain M > m independent bit commitments using m initial information theoretic bit commitments. We also discuss related proposals, in particular, we analyse the quantum bit escrow of Ta-Shma, Vazirani and Yao, the cheat-sensitive bit commitment of Hardy and Kent, and the relativistic bit commitment of Kent.