PSPACE has 2-round quantum interactive proof systems

TL;DR

This paper proves that every language in PSPACE has a two-round quantum interactive proof system with exponentially small error, demonstrating that quantum proofs are more powerful than classical ones in constant rounds unless the polynomial hierarchy collapses.

Contribution

It establishes that PSPACE languages have efficient two-round quantum interactive proof systems, highlighting a separation from classical proof systems under certain complexity assumptions.

Findings

Quantum interactive proof systems can recognize all PSPACE languages.

Two-round quantum proofs have exponentially small error probability.

Quantum proofs are strictly more powerful than classical proofs in constant rounds.

Abstract

In this paper we consider quantum interactive proof systems, i.e., interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. It is proved that every language in PSPACE has a quantum interactive proof system that requires only two rounds of communication between the prover and verifier, while having exponentially small (one-sided) probability of error. It follows that quantum interactive proof systems are strictly more powerful than classical interactive proof systems in the constant-round case unless the polynomial time hierarchy collapses to the second level.