Impossibility of quantum string commitment under Holevo information
Rahul Jain · arXiv (Cornell University) · 2005
We show a new impossibility result for Quantum string commitment (QSC) schemes (introduced in [BCH+ 05]). For a single execution of protocol we show binding-concealing trade-offs in terms of the well known and studied Holevo-χ information. Our result is an improvement over the result of [BCH+ 05] who, for a single execution of the protocol, showed binding-concealing trade-offs in terms of a quantity introduced by them called the One shot Holevo-Ξ information (please refer to Section 1 for definition). We consider our result as an improvement since for any ensemble E, Ξ(E) ≥ χ(E). The significance of our result arises from the fact that the trade-off is shown in terms of the well studied Holevo-χ information. We show our result by making a central use of an important information theoretic tool called the substate theorem [JRS02]. Our technique is quite different from that of [BCH+ 05] and is of independent interest. It will be interesting to see if this technique finds other applications. We also show a worst case binding-concealing tradoff in terms of the maximum possible information of the encoding derived from the protocol. This result is completely new and nothing similar has been shown in [BCH+ 05]. 1