Quantum key distribution based on orthogonal states allows secure quantum bit commitment

Abstract

For more than a decade, it was believed that unconditionally secure quantum bit commitment (QBC) is impossible. But based on a previously proposed quantum key distribution scheme using orthogonal states, here we build a QBC protocol in which the density matrices of the quantum states encoding the commitment do not satisfy a crucial condition on which the no-go proofs of QBC are based. Thus, the no-go proofs could be evaded. Our protocol is fault-tolerant and very feasible with currently available technology. It reopens the venue for other ‘post-cold-war’ multi-party cryptographic protocols, e.g. quantum bit string commitment and quantum strong coin tossing with an arbitrarily small bias. This result also has a strong influence on the Clifton–Bub–Halvorson theorem which suggests that quantum theory could be characterized in terms of information-theoretic constraints.

Can relativistic bit commitment lead to secure quantum oblivious transfer?

“…But here we can see that its power is not limited to the QBC protocol in Ref. [45]. Especially, Bob's steps related with Eqs.…”

“…On the other hand, if a protocol can further force Charlie to commit to a particular classical x, i.e., besides p 0 + p 1 → 1, both p 0 and p 1 can only take the values 0 or 1 instead of any value in between, then it is called a bit commitment with a certificate of classicality (BCCC). All the above mentioned BC protocols [39][40][41][42]45] are not BCCC, and unconditionally secure BCCC seems impossible [46]. Therefore, in the following when speaking of secure BC, we refer to the non-BCCC ones only, except where noted.…”

“…That is, no matter we use relativistic BC [39][40][41][42], or "practical" QBC protocols listed in the introduction of Ref. [45], we assume that all the security requirements (e.g., relativistic settings or experimental limitations) are already met, so that Bob does not have unlimited computational power to cheat within the BC stage. In this case, the validity of the no-go proofs of QOT [30][31][32][33][34][35][36][37][38] cannot be taken for granted, because all these proofs were derived without implying any limitation on the computational power of the cheater.…”

“…[45], which was applied to show why the specific QBC protocol in the same reference cannot lead to secure QOT. But here we can see that its power is not limited to the QBC protocol in Ref.…”

Local distinguishability of generic unentangled orthonormal bases

“…Thus, such states encode quantum nonlocality. It is demonstrably useful in quantum key distribution (QKD), as first observed by Goldenberg and Vaidman [5], and since used in other schemes for secure communication [6,7]. * Jiří Lebl was partially supported by NSF grant DMS-1362337 and Oklahoma State University's DIG and ASR grants.…”