bibkey: qian2025nonlocalnonstabilizerness authors: Dongheng Qian; Jing Wang year: 2025 title: “Quantum non-local nonstabilizerness” doi: 10.1103/PhysRevA.111.052443 url: https://arxiv.org/abs/2502.06393v4 claim: “Appendix F conjectures that some separable multi-qubit states cannot be brought into STAB by local unitaries.” strata_touched:
- D5/S3/Quantum/Information/SeparableStateLocalUnitaryStabilizerObstruction license: citation-only triage: anchor
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DOI: 10.1103/PhysRevA.111.052443
Source: https://arxiv.org/abs/2502.06393v4
Crossref identifies Dongheng Qian and Jing Wang, Quantum nonlocal nonstabilizerness, Physical Review A 111, 052443 (2025), at this DOI. The arXiv title includes the hyphen in “non-local”.
Appendix F, PDF p. 8, states:
However, we are unaware of any proof guaranteeing that every separable multi-qubit state can be transformed into a state belonging to STAB using only local unitary transformations, and we conjecture that this is not the case.
On the same page, equation (F1) is introduced by:
A separable state is defined as the convex hull of pure product states [1]:
The distinction between STAB and STAB₀ is explicit. The sentence preceding (F2) says:
while STAB is defined as the convex hull of pure stabilizer states:
Equation (F2) is
followed by:
where ψᵢ are pure stabilizer states.
The probabilities are nonnegative and sum to one, as specified by the convex-hull definition. Equation (F4) gives the numerical example
The source reports the numerical local-unitary minimum . This reported decimal is not an exact certificate. The conjecture concerns the full convex stabilizer hull STAB, rather than the smaller set STAB₀ of normalized commuting-Pauli subgroup projectors.