  String commitment schemes are similar to the well studied bit commitment
schemes in cryptography with the difference that the committing party, say
Alice, is supposed to commit a long string instead of a single bit, to another
party say Bob. Similar to bit commitment schemes, such schemes are supposed to
be binding, i.e Alice cannot change her choice after committing, and concealing
i.e. Bob cannot find Alice's committed string before Alice reveals it.
  Ideal commitment schemes are known to be impossible. Even if some degrees of
cheating is allowed, Buhrman, Christandl, Hayden, Lo and Wehner
(quant-ph/0504078) have recently shown that there are some binding-concealing
trade-offs that any quantum string commitment scheme (QSC) must follow. They
showed trade-offs both in the scenario of single execution of the protocol and
in the asymptotic regime of sufficiently large number of parallel executions of
the protocol.
  We present here new trade-offs in the scenario of single execution of a QSC
protocol. Our trade-offs also immediately imply the trade-off shown by Buhrman
et al. in the asymptotic regime. We show our results by making a central use of
an important information theoretic tool called the substate theorem due to
Jain, Radhakrishnan and Sen. Our techniques are quite different from that of
Buhrman et al. and may be of independent interest.

Quantum Physics