QIP = IP

QIP is equal to IP.

Statement

Migrated verbatim from quantum-interactive-proofs § Known relationships:

• $\mathbf{QIP}=\mathbf{PSPACE}$ — TODO citation (Jain, Ji, Upadhyay, Watrous 2010). Since $\mathbf{IP}=\mathbf{PSPACE}$ as well, quantum interactive proofs are no more powerful than classical interactive proofs. This is a striking collapse: quantum communication between prover and verifier adds no power to multi-round interactive proofs.

Notes

source: folklore: the claim carried no citation on the page it was migrated from, and none was invented.

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

class: free because a containment between complexity classes is proved by any argument at all; the reduction-class axis does not discriminate here, and unstated would wrongly suggest the information is missing.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• Derived from the two equalities rather than independently proved; nothing marks it as derived.
• Uncited.
• The sentence carrying it (‘This is a striking collapse …’) is editorializing, a house-style anti-pattern.