Log-depth circuits suffice for average-case single-copy stabilizer learning with t=O(log n), but worst-case adaptive single-copy learning requires exp(t) samples.
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A new third-order separability witness constructs a 4x4 matrix from local randomized measurement invariants whose negative minimum eigenvalue certifies entanglement with dimension-independent sample complexity.
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Single-copy stabilizer learning: average case and worst case
Log-depth circuits suffice for average-case single-copy stabilizer learning with t=O(log n), but worst-case adaptive single-copy learning requires exp(t) samples.
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Third-Order Local Randomized Measurements for Finite-size Entanglement Certification
A new third-order separability witness constructs a 4x4 matrix from local randomized measurement invariants whose negative minimum eigenvalue certifies entanglement with dimension-independent sample complexity.