Entanglement and interference are among the most fundamental properties of quantum mechanics. In this work, we investigate the role and power of interference in the context of detecting entanglement. We do so from a computational complexity lens by proving that unentanglement gives no additional power to stoquastic Merlin-Arthur verification. For every polynomial number of provers $k=k(n)$, \[ \text{StoqMa}(k)=\text{StoqMa} . \] Conceptually, the proof separates the role of entanglement from the role of interference: once destructive interference is ruled out by stoquasticity, the product-state constraint can be absorbed into a polynomially larger one-witness stoquastic verification. The main analytic ingredient is a positive, value-based de Finetti theorem for separately symmetric extensions. If $M$ is an entrywise nonnegative positive semidefinite contraction on $A_1\otimes\cdots\otimes A_k$, then the nonnegative product value of $M$ is approximated to additive error $ε$ by the largest eigenvalue of \[ Π_R^{<k} (M_{A_{1,1}\cdots A_{k-1,1}A_k}\otimes I) Π_R^{<k}, \qquad R=O\!\left(\frac{k^2\sum_i\log\dim A_i}{ε^3}\right), \] where $Π_R^{<k}$ is the operator on $A_1^{\otimes R} \otimes \cdots \otimes A_{k-1}^{\otimes R} \otimes A_k$ projecting to the subspace $\mathrm{Sym}^R(A_1) \otimes \cdots \otimes \mathrm{Sym}^{R}(A_{k-1}) \otimes A_k$. The spectral relaxation is then realized as an actual one-witness stoquastic verifier. After replacing the uniform permutation averages in the symmetric projectors by inverse-polynomially close dyadic inverse-invariant averages. Consequently, \[ \text{StoqMa}(k)=\text{StoqMa}\subseteq\text{AM}\cap\text{PP}\subseteq\text{PSPACE} . \] The positive de Finetti theorem is isolated as a standalone technique and may be useful in other nonnegative tensor-optimization and stoquastic-verification settings.

翻译：纠缠和干涉是量子力学最基本的性质之一。本文从检测纠缠的视角出发，研究干涉的作用和力量。我们通过计算复杂度的透镜进行分析，证明非纠缠并未给停高斯梅林-亚瑟验证带来额外能力。对于任意多项式数量的证明者 $k=k(n)$，有 \[ \text{StoqMa}(k)=\text{StoqMa} . \] 概念上，该证明将纠缠的作用与干涉的作用分离开来：一旦通过停高斯性排除了相消干涉，乘积态约束可被吸收进一个多项式规模更大的单证明者停高斯验证中。主要分析工具是用于分别对称扩展的正值、基于值的德菲内蒂定理。若 $M$ 是 $A_1\otimes\cdots\otimes A_k$ 上逐项非负的正半定压缩算子，则 $M$ 的非负乘积值在加法误差 $ε$ 内由以下算子的最大特征值逼近： \[ Π_R^{<k} (M_{A_{1,1}\cdots A_{k-1,1}A_k}\otimes I) Π_R^{<k}, \qquad R=O\!\left(\frac{k^2\sum_i\log\dim A_i}{ε^3}\right), \] 其中 $Π_R^{<k}$ 是 $A_1^{\otimes R} \otimes \cdots \otimes A_{k-1}^{\otimes R} \otimes A_k$ 上投影到子空间 $\mathrm{Sym}^R(A_1) \otimes \cdots \otimes \mathrm{Sym}^{R}(A_{k-1}) \otimes A_k$ 的算子。该谱松弛随后被实现为实际单证明者停高斯验证器。通过将对称投影子中的均匀置换平均替换为逆多项式接近的二进逆不变平均，得到： \[ \text{StoqMa}(k)=\text{StoqMa}\subseteq\text{AM}\cap\text{PP}\subseteq\text{PSPACE} . \] 该正值德菲内蒂定理被提炼为独立技术，可能对其他非负张量优化和停高斯验证场景具有普适价值。