  To evade the well-known impossibility of unconditionally secure quantum
two-party computations, previous quantum private comparison protocols have to
adopt a third party. Here we study how far we can go with two parties only. We
propose a very feasible and efficient protocol. Intriguingly, although the
average amount of information leaked cannot be made arbitrarily small, we find
that it never exceeds 14 bits for any length of the bit-string being compared.
