(B1) The purity of this state is given by tr EP |ψ⟩⟨ψ|⊗α 2 = d−4 d2−1 ∑ j,k=0 tr Pj|ψ⟩⟨ψ|PjPk|ψ⟩⟨ψ|Pk α = d−4 d2−1 ∑ j,k=0 ⟨ψ| PjPk|ψ⟩⟨ψ|PkPj |ψ⟩ α

Aα(|ψ⟩) from the purity of EP (|ψ⟩⟨ψ|⊗α)’s output Here, we provide the proof of how Aα(|ψ⟩) is encoded into the purity of the state EP |ψ⟩⟨ψ|⊗α = d−2 d2−1 ∑ j=0 Pj|ψ⟩⟨ψ|Pj ⊗α

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An Algorithm for Estimating $\alpha$-Stabilizer R\'enyi Entropies via Purity

quant-ph · 2025-07-03 · unverdicted · novelty 7.0

Introduces a purity-encoding algorithm for estimating α-Stabilizer Rényi Entropies of unknown quantum states for integer α > 1, with benchmarks and a non-stabilizerness/entanglement link.

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An Algorithm for Estimating $\alpha$-Stabilizer R\'enyi Entropies via Purity quant-ph · 2025-07-03 · unverdicted · none · ref 28
Introduces a purity-encoding algorithm for estimating α-Stabilizer Rényi Entropies of unknown quantum states for integer α > 1, with benchmarks and a non-stabilizerness/entanglement link.

(B1) The purity of this state is given by tr EP |ψ⟩⟨ψ|⊗α 2 = d−4 d2−1 ∑ j,k=0 tr Pj|ψ⟩⟨ψ|PjPk|ψ⟩⟨ψ|Pk α = d−4 d2−1 ∑ j,k=0 ⟨ψ| PjPk|ψ⟩⟨ψ|PkPj |ψ⟩ α

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