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Sample complexity First, consider the estimator bz(θ) = 1 Nshot NshotX ℓ=1 Xℓ, X ℓ = exp h i √ 3θ(n3,ℓ −n 2,ℓ) i ,(143), it’s unbiased, namely,E bz(θ) =z(θ)

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quant-ph 1

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2026 1

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CONDITIONAL 1

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Uncovering Non-Gaussianity through Multi-Copy Symmetries

quant-ph · 2026-08-04 · conditional · novelty 6.0

For any Gaussian single-mode state and any orthogonal copy-mixing matrix fixing the symmetric collective mode, Tr(ρ^⊗k Γ(O)) = (1-λ)^k/det(I_k - λO); violation of this identity certifies non-Gaussianity.

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  • Uncovering Non-Gaussianity through Multi-Copy Symmetries quant-ph · 2026-08-04 · conditional · none · ref 1

    For any Gaussian single-mode state and any orthogonal copy-mixing matrix fixing the symmetric collective mode, Tr(ρ^⊗k Γ(O)) = (1-λ)^k/det(I_k - λO); violation of this identity certifies non-Gaussianity.