Paper 2020/1488

General Properties of Quantum Bit Commitments

Jun Yan

Abstract

While unconditionally-secure quantum bit commitment (allowing quantum computation and quantum communication) is impossible, in this work we study complexity-based quantum bit commitment. In particular, we will study its general properties through the lens of the so-called ``canonical" quantum bit commitment schemes. The reason why we can do this is that as will be shown in this work, any complexity-based quantum bit commitment scheme can be converted into the canonical form. Both flavors of canonical quantum bit commitment schemes (i.e. computationally hiding and statistically binding, or statistically hiding and computationally binding), which will be shown equivalent in this work, can be based on quantum-secure one-way functions (or pseudorandom quantum states by more recent results). But in our opinion, the question of whether canonical quantum bit commitment schemes exist is interesting in its own right in quantum complexity theory and may serve as an alternative foundation of complexity-based quantum cryptography.