For odd prime qudits, the sample complexity of direct fidelity estimation is controlled by the Wigner rank and mana of the target state or channel, with constant measurement settings and efficient protocols for stabilizer and low-magic targets.
Efficient classical simulation of clifford circuits with nonstabilizer input states
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Quantum Fidelity Estimation in the Resource Theory of Nonstabilizerness
For odd prime qudits, the sample complexity of direct fidelity estimation is controlled by the Wigner rank and mana of the target state or channel, with constant measurement settings and efficient protocols for stabilizer and low-magic targets.