Zero-Knowledge (ZK) protocols have been intensely studied due to their
fundamental importance and versatility. However, quantum information's inherent
differences significantly alter the landscape, necessitating a re-examination
of ZK designs.
A crucial aspect is round complexity, linked to
simulation, which
forms the foundation of ZK definition and security proofs. In the
post-quantum setting, where honest parties and channels are
classical but adversaries quantum, Chia et al. [FOCS'21] showed constant-round
black-box-simulatable ZK arguments (BBZK) for
NP are
impossible unless
NP⊆BQP. But this problem
remains open when all parties and communication are quantum.
Indeed, this problem interests the broader theory of quantum computing.
Investigating how quantum power alters tasks like the
unconditional
security of QKD and incorporating OT in MiniQCrypt has been crucial. Moreover,
quantum communication has enabled round compression for commitments and
interactive arguments. Along this line, understanding if quantum computing
could fundamentally change ZK protocols is vital.
We resolved this problem by proving that only languages in
BQP
admit constant-round
fully-quantum BBZK. This result holds
significant implications. Firstly, it illuminates the nature of quantum
zero-knowledge and provides valuable insights for designing future protocols in
the quantum realm. Secondly, it relates ZK round complexity with the intriguing
problem of
BQP vs
QMA, which is out of the reach of
previous analogue impossibility results in the classical or post-quantum
setting. Lastly, it justifies the need for the
non-black-box
simulation techniques or the relaxed security notions employed in existing
constant-round fully-quantum BBZK protocols.