Certifying unknown-basis pure-state entanglement dimensionality with few measurement settings

Abstract:We introduce a basis-independent algorithm that only uses single-copy measurements to certify the Schmidt number of $2n$-qubit bipartite pure states. Assuming the local system dimension is $d = 2^n$, the Schmidt number $\chi$ is $O(1)$, and the non-zero Schmidt coefficients are bounded below by $\Omega(1)$, our protocol achieves a total sample complexity of $\widetilde{O}(d^2\chi^2)$ with only $\widetilde{O}(\chi^4)$ measurement settings. This work establishes a measurement-setting-efficient approach to high-dimensional entanglement certification.

arXiv:2601.11040 [quant-ph]

(or arXiv:2601.11040v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2601.11040 Focus to learn more arXiv-issued DOI via DataCite

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