Algorithms achieve near-optimal quantum state certification with limited entanglement (t=d^2 copies), plus similar results for mixedness testing and purity estimation, supported by lower bounds.
[NTGK25] Jan N¨ oller, Viet T Tran, Mariami Gachechiladze, and Richard Kueng
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Optimal Quantum State Testing Even with Limited Entanglement
Algorithms achieve near-optimal quantum state certification with limited entanglement (t=d^2 copies), plus similar results for mixedness testing and purity estimation, supported by lower bounds.