Universal two-copy quantum state purification under depolarizing noise requires magic resources that scale linearly with the fidelity gain, establishing an exact resource law for odd dimensions and tight bounds for multi-qubit systems.
For prime dimensiond, the unitary boost and shift operatorsX, Z∈ L(H)are defined by X|j⟩=|j⊕1⟩, Z|j⟩=ω j|j⟩,(S1) whereω=e 2πi/d and⊕denotes addition modulod
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A Nonstabilizerness Resource Law for Universal Quantum State Purification
Universal two-copy quantum state purification under depolarizing noise requires magic resources that scale linearly with the fidelity gain, establishing an exact resource law for odd dimensions and tight bounds for multi-qubit systems.