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Quantum Merlin-Arthur with an Internally Separable Proof

Authors Roozbeh Bassirian , Bill Fefferman , Itai Leigh , Kunal Marwaha , Pei Wu

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Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
  • Theory of computation → Interactive proof systems
  • Theory of computation → Complexity classes
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Quantum complexity theory
Keywords
  • entanglement structures
  • unentanglement
  • quantum complexity
  • QMA(2)
  • NEXP

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Abstract

While the role of entanglement in quantum proof systems has been extensively studied, the computational power of unentanglement remains poorly understood. Since entanglement admits many inequivalent multipartite structures, it is natural to ask how more fine-grained structural promises affect computational power. In this work we investigate a mild promise: each proof is internally separable, meaning that after tracing out one register, a designated constant-size subsystem is separable from the rest - even though the overall proof may still be entangled across every bipartition. We prove a qualitative jump from one proof to two: with one internally separable proof, the resulting class is contained in EXP (even allowing an inverse-exponential completeness–soundness gap), whereas with two unentangled internally separable proofs, the class equals NEXP at constant gap. Notably, in the NEXP construction, the second proof is used solely to implement a SWAP-based purity test.

Cite As Get BibTex

Roozbeh Bassirian, Bill Fefferman, Itai Leigh, Kunal Marwaha, and Pei Wu. Quantum Merlin-Arthur with an Internally Separable Proof. In 21st Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 389, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.TQC.2026.5

Author Details

Roozbeh Bassirian
  • University of Chicago, IL, USA
Bill Fefferman
  • University of Chicago, IL, USA
Itai Leigh
  • Tel Aviv University, Israel
Kunal Marwaha
  • University of Chicago, IL, USA
Pei Wu
  • Pennsylvania State University, University Park, PA, USA

Funding

This work was done in part while a subset of the authors were visiting the Simons Institute for the Theory of Computing, supported by NSF QLCI Grant No. 2016245. BF, RB, and KM acknowledge support from AFOSR (FA9550-21-1-0008). This material is based upon work partially supported by the National Science Foundation under Grant CCF-2044923 (CAREER), by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers (Q-NEXT) and by the DOE QuantISED grant DE-SC0020360. Any views, opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation, European Union, or the European Research Council Executive Agency. Neither the European Union nor any granting authority can be held responsible for them.
  • Leigh, Itai: co-funded by the European Union (ERC, EACTP, 101142020), the Israel Science Foundation (grant number 514/20) and the Len Blavatnik and the Blavatnik Family Foundation.
  • Marwaha, Kunal: acknowledges support from the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1746045.

Acknowledgements

KM thanks Tyler Chen, Christopher Musco, and Apoorv Vikram Singh for helpful discussions on convex optimization. RB, KM, and IL thank the Institute for Advanced Study for organizing the summer school where they met and began collaborating. IL and PW thank Thomas Vidick for suggesting them to talk.

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