SZK ⊆ QSZK

Inclusion · quantum setting · Wat02, Wat06

Statement

$\mathbf{SZK}\subseteq \mathbf{QSZK}$: SZK lies in the honest-verifier class $\mathbf{HVQSZK}$ of Wat02, and $\mathbf{HVQSZK}$ equals QSZK, where zero knowledge is required against arbitrary quantum verifiers — Wat06.

Sketch

A classical statistical zero-knowledge proof system, run by quantum parties, is an honest-verifier quantum statistical zero-knowledge proof system whose messages and simulator output are classical.

Notes

• The equality $\mathbf{HVQSZK}=\mathbf{QSZK}$ rests on quantum rewinding — Wat06.