Equilibrium Value Method for the Proof of QIP=PSPACE

Weprovide an alternative proof of QIP=PSPACE to the recent breakthrough result [JJUW09]. Unlike solving some semidefinite programs that captures the computational power of quantum interactive proofs, our method starts with one QIP-Complete problem which computes the diamond norm between two admissible quantum channels. The key observation is that we can convert the computation of the diamond norm into the computation of some equilibrium value. The later problem, different from semidefinite programs, is of better form, easier to solve and could be interesting for its own sake. The multiplicative weight update method is also applied to solve the equilibrium value problem, however, in a relatively simpler way than the one in the original proof [JJUW09]. Furthermore, we provide a generalized form of equilibrium value problems which can be solved in the same way as well as comparisons to semidefinite programs.