New Binding-Concealing Trade-Offs for Quantum String Commitment

Xin Sun, Quanlong Wang, Feifei He

Nir Bitansky, Zvika Brakerski

Li Yang, Chong Xiang, Bao Li

Several kinds of qubit-string-based(QS-based) bit commitment protocols are presented, and a definition of information-theoretic concealing is given. All the protocols presented here are proved to be secure under this definition. We suggest an attack algorithm to obtain the local unitary transformation introduced in no-go theorem, which is used to attack the binding condition, then study the security of our QS-based bit commitment protocols under this attack via introducing a new concept "physical security of protocol". At last we present a practical QS-based bit commitment scheme against channel loss and error.

David Peter Divincenzo, John A. Smolin, Barbara M. Terhal

Security trade-offs have previously been established for one-way bit commitment. We study this trade-off in two superselection settings. We show that for an [lsquo]abelian[rsquo] superselection rule (exemplified by particle conservation), the standard trade-off between sealing and binding properties still holds. For the non-abelian case (exemplified by angular momentum conservation), the security trade-off can be more subtle, which we illustrate by showing that if the bit commitment is forced to be ancilla-free, an asymptotically secure quantum bit commitment is possible.

Dominique Unruh

Robert W. Spekkens, Terry Rudolph

Although it is impossible for a bit commitment protocol to be both arbitrarily concealing and arbitrarily binding, it is possible for it to be both partiallyconcealing and partiallybinding. This means that Bob cannot, prior to the beginning of the unveiling phase, find out everything about the bit committed, and Alice cannot, through actions taken after the end of the commitment phase, unveil whatever bit she desires. We determine upper bounds on the degrees of concealment and bindingness that can be achieved simultaneously in anybit commitment protocol, although it is unknown whether these can be saturated. We do, however, determine the maxima of these quantities in a restricted class of bit commitment protocols, namely, those wherein all the systems that play a role in the commitment phase are supplied by Alice. We show that these maxima can be achieved using a protocol that requires Alice to prepare a pair of systems in an entangled state, submit one of the pair to Bob at the commitment phase, and the other at the unveiling phase. Finally, we determine the form of the trade off that exists between the degree of concealment and the degree of bindingness given various assumptions about the purity and dimensionality of the states used in the protocol.