Quantum bit commitment is impossible, but how far can we stretch the quantum limits when the task is to commit a string of n bits rather than a single bit? ”Not very far” is the answer that we obtain a from a no-go argument, where we invoke the Holevo information as the security criterion. In particular, our result implies the optimality of the trivial scheme, in which Alice sends a subset of b bits to Bob (commit phase) and later reveals the remaining n-b bits. Things change dramatically, however, if we are willing to revise our standard of security and use the accessible information instead of the Holevo information. Based on the phenomenon of ”locking” classical information into quantum states, we are able to design protocols which impose strong limitations on the ability of both parties to cheat.

This is joint work with Matthias Christandl, Patrick Hayden, Hoi-Kwong Lo and Stephanie Wehner.