Degrees of concealment and bindingness in quantum bit commitment protocols
By Robert W. Spekkens, Terry Rudolph. 2001
156 citations recorded by the source corpus.
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 partially concealing and partially binding. 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 any bit 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.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/7fdd179c9a0a5d32f6f5226c75ec7109c6ad370b
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In Artificial Intelligence
- Roger Colbeck
- John Watrous
- Robert W. Spekkens
- Renato Renner
- Gilad Gour
- Eric Chitambar
- Miriam Backens
- Bob Coecke
In Atomic and Molecular Physics, and Optics
- Roger Colbeck
- John Watrous
- Robert W. Spekkens
- Gilad Gour
- Eric Chitambar
- Christopher A. Fuchs
- Miriam Backens
- C. Ferrie
Citations in the corpus
- The Theory of Quantum Information (2018, background): “32 is due to Spekkens and Rudolph [196], and Theorem 3.”
- Quantum And Relativistic Protocols For Secure Multi-Party Computation (2009, background): “Furthermore, there cannot be a bit-commitment based scheme of this type(6) with a smaller dimensionality than Ambainis’ since bit-commitment based protocols using qubits cannot achieve bias 1 4 [47].”
- Evidence for the epistemic view of quantum states: A toy theory (2004, background): “Moreover, it is likely that arbitrarily concealing and arbitrarily binding bit commitment [65, 66] is not possible in the toy theory.”