The Collapse of Unentangled Stoquastic Merlin-Arthur Proof Systems
Abstract
Interference and entanglement are among the most fundamental properties of quantum mechanics. In this work, we investigate the power of interference in the role of detecting entanglement in the context of quantum Merlin-Arthur verification. In particular, we show that unentanglement gives no additional power to stoquastic Merlin-Arthur proof systems, whose restriction to a classical gate set results in entrywise non-negative acceptance operators and non-negative optimal witnesses, therein removing destructive interference from the verification process. Our results show that for any polynomial number of unentangled witnesses k = k(n), StoqMA(k) = StoqMA. The analytic core of this result is a new non-negative de Finetti theorem for separately bosonic states. If a mixed state ρ is supported on the tensor product of symmetric subspaces of ℋ1⊗ R ⊗ ℋ2⊗ R ⊗ ⋯ ⊗ ℋk⊗ R then there exists a separable state τ on ℋ1 ⊗ ⋯ ⊗ ℋk such that Tr(M(ρℋ1 ⊗ ⋯ ⊗ ℋk − τ)) ≤ 2 √((k log2dim(ℋ1 ⊗ ⋯ ⊗ ℋk))/(R−1)), simultaneously for all non-negative effects M. For any such operator M, one can define the separately symmetric lift SSR(M) whose largest eigenvalue approximates the maximum acceptance probability of M over product states within the same error bound. Such a lift can be approximated by a stoquastic verifier, giving that product-state constraint of StoqMA(k) verifiers can be absorbed into a polynomially larger one-witness StoqMA verification, while preserving an inverse polynomial completeness-soundness gap.
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BibTeX
@misc{gay2026collapse,
title = {{The Collapse of Unentangled Stoquastic Merlin-Arthur Proof Systems}},
author = {William Gay and Fernando Granha Jeronimo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.16249},
eprint = {2605.16249},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.16249},
}
RIS
TY - UNPB
TI - The Collapse of Unentangled Stoquastic Merlin-Arthur Proof Systems
AU - William Gay
AU - Fernando Granha Jeronimo
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2605.16249
UR - https://arxiv.org/abs/2605.16249
AB - Interference and entanglement are among the most fundamental properties of quantum mechanics. In this work, we investigate the power of interference in the role of detecting entanglement in the context of quantum Merlin-Arthur verification. In particular, we show that unentanglement gives no additional power to stoquastic Merlin-Arthur proof systems, whose restriction to a classical gate set results in entrywise non-negative acceptance operators and non-negative optimal witnesses, therein removing destructive interference from the verification process. Our results show that for any polynomial number of unentangled witnesses k = k(n), StoqMA(k) = StoqMA. The analytic core of this result is a new non-negative de Finetti theorem for separately bosonic states. If a mixed state ρ is supported on the tensor product of symmetric subspaces of ℋ_1^⊗ R ⊗ ℋ_2^⊗ R ⊗ ⋯ ⊗ ℋ_k^⊗ R then there exists a separable state τ on ℋ_1 ⊗ ⋯ ⊗ ℋ_k such that Tr(M(ρ_ℋ_1 ⊗ ⋯ ⊗ ℋ_k − τ)) ≤ 2 √((k log_2dim(ℋ_1 ⊗ ⋯ ⊗ ℋ_k))/(R−1)), simultaneously for all non-negative effects M. For any such operator M, one can define the separately symmetric lift SS_R(M) whose largest eigenvalue approximates the maximum acceptance probability of M over product states within the same error bound. Such a lift can be approximated by a stoquastic verifier, giving that product-state constraint of StoqMA(k) verifiers can be absorbed into a polynomially larger one-witness StoqMA verification, while preserving an inverse polynomial completeness-soundness gap.
ER -