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PreprintarXiv licencearXiv

Beyond IP = PSPACE and QIP = PSPACE: Interactive Proofs in Arbitrary Physical Theories

  • Kishor Bharti
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Abstract

The equalities IP = PSPACE and QIP = PSPACE, the latter achievable with three messages, raise a basic question: how much of an interactive proof's power comes from the underlying physical theory? We study interactive proofs in general probabilistic theories, which include classical and quantum theory. The answer depends on what the prover and verifier exchange and how the theory specifies efficient operations. When they exchange only classical messages, protocols in every theory satisfying our standard assumptions decide exactly PSPACE. For protocols with a quantum verifier and quantum messages, allowing a prover to use any theory containing quantum theory does not increase the maximum acceptance probability. Thus, the three-message PSPACE result remains valid against such provers. When messages may be arbitrary systems, the interactive-proof class can strictly exceed PSPACE.

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Cite

BibTeXRIS
BibTeX
@misc{bharti2026beyond,
  title = {{Beyond IP = PSPACE and QIP = PSPACE: Interactive Proofs in Arbitrary Physical Theories}},
  author = {Kishor Bharti},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00847},
  eprint = {2610.00847},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00847},
}
RIS
TY  - UNPB
TI  - Beyond IP = PSPACE and QIP = PSPACE: Interactive Proofs in Arbitrary Physical Theories
AU  - Kishor Bharti
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00847
UR  - https://arxiv.org/abs/2610.00847
AB  - The equalities IP = PSPACE and QIP = PSPACE, the latter achievable with three messages, raise a basic question: how much of an interactive proof's power comes from the underlying physical theory? We study interactive proofs in general probabilistic theories, which include classical and quantum theory. The answer depends on what the prover and verifier exchange and how the theory specifies efficient operations. When they exchange only classical messages, protocols in every theory satisfying our standard assumptions decide exactly PSPACE. For protocols with a quantum verifier and quantum messages, allowing a prover to use any theory containing quantum theory does not increase the maximum acceptance probability. Thus, the three-message PSPACE result remains valid against such provers. When messages may be arbitrary systems, the interactive-proof class can strictly exceed PSPACE.
ER  -