  Zero-knowledge and multi-prover systems are both central notions in classical
and quantum complexity theory. There is, however, little research in quantum
multi-prover zero-knowledge systems. This paper studies complexity-theoretical
aspects of the quantum multi-prover zero-knowledge systems. This paper has two
results:
  1.QMIP* systems with honest zero-knowledge can be converted into general
zero-knowledge systems without any assumptions.
  2.QMIP* has computational quantum zero-knowledge systems if a natural
computational conjecture holds.
  One of the main tools is a test (called the GHZ test) that uses GHZ states
shared by the provers, which prevents the verifier's attack in the above two
results. Another main tool is what we call the Local Hamiltonian based
Interactive protocol (LHI protocol). The LHI protocol makes previous research
for Local Hamiltonians applicable to check the history state of interactive
proofs, and we then apply Broadbent et al.'s zero-knowledge protocol for QMA
\cite{BJSW} to quantum multi-prover systems in order to obtain the second
result.
