Unconditional lower bounds and matching (or nearly matching) upper bounds are proved for public- and private-coin distributed quantum state certification under joint classical-plus-quantum communication limits.
[Hay98] Masahito Hayashi
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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.
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Distributed Property Testing with (Quantum) Carrier Pigeons: Tight Bounds on State Certification
Unconditional lower bounds and matching (or nearly matching) upper bounds are proved for public- and private-coin distributed quantum state certification under joint classical-plus-quantum communication limits.
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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.