Certifying entanglement dimensionality by random Pauli sampling

Changhao Yi

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arXiv · 2601.11040

Certifying entanglement dimensionality by random Pauli sampling

Changhao Yi

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Abstract

We introduce a Pauli-measurement-based algorithm to certify the Schmidt number of $n$-qubit pure states. Our protocol achieves an average-case sample complexity of $\caO(\mathrm{poly}(n)\chi^2)$, a substantial improvement over the $\caO(2^n \chi)$ worst-case bound. By utilizing local pseudorandom unitaries, we ensure the worst case can be transformed into the average-case with high probability. This work establishes a scalable approach to high-dimensional entanglement certification and introduces a proof framework for random Pauli sampling.

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Changhao Yi. 2026-01-16. Certifying entanglement dimensionality by random Pauli sampling. https://arxiv.org/abs/2601.11040

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