Class Description

HVSZK: Honest-Verifier SZK

The class of decision problems that have SZK protocols assuming an honest verifier (i.e. one who doesn't try to learn more about the problem by deviating from the protocol).

Equals SZK [Oka96].

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QSZK: Quantum Statistical Zero-Knowledge

A quantum analog of SZK (or more precisely HVSZK).

Arthur is a BQP (i.e. quantum) verifier who can exchange quantum messages with Merlin. So Arthur and Merlin's states may become entangled during the course of the protocol.

Arthur's "view" of his interaction with Merlin is taken to be the sequence of mixed states he has, over all steps of the protocol. The zero-knowledge requirement is that each of these states must have trace distance at most (say) 1/10 from a state that Arthur could prepare himself (in BQP), without help from Merlin. Arthur is assumed to be an honest verifier.

Defined in [Wat02], where the following was also shown:

Subsequently, [Wat09b] showed that honest-verifier and general-verifier quantum statistical zero-knowledge are equivalent.

There exists an oracle relative to which QSZK does not contain UPcoUP, and a random oracle relative to which QSZK does not contain UP [MW18].

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