Trustworthiness of nonclassicality assessments on theory-agnostic GPT shadows

Determine whether assessments of nonclassicality performed on generalized probabilistic theory fragments constructed via theory-agnostic tomography are trustworthy, despite the possibility that such fragments constitute GPT shadows that can invalidate simplex-embeddability-based assessments.

Background

Theory-agnostic tomography reconstructs a generalized probabilistic theory fragment directly from observed prepare-and-measure statistics without assuming quantum theory. The paper notes that these reconstructed fragments can be GPT shadows, which may differ from the underlying GPT in ways that affect nonclassicality certification.

The unresolved issue is whether a nonclassicality assessment applied to such a reconstructed shadow reliably reflects the nonclassicality of the underlying physical experiment. The authors use a fully dephased classical counterpart as a consistency check, but this numerical check does not resolve the general question.

References

As previously established, it is an open question whether the assessment of nonclassicality over a GPT constructed via theory-agnostic tomography is trustworthy.

— Theory-agnostic nonclassicality certification in an integrated photonic circuit  (2609.18671 - Rossi et al., 16 Sep 2026) in Appendix, Section 'Consistency check' (Appendix section label not specified)

Moreover, the fact that the optimal rank for theory-agnostic tomography may be smaller than the GPT dimension suggested by the underlying quantum system could help circumvent the conjectured exponential complexity of simplex-embeddability certification, since the theory-agnostic GPT fragment can live in a smaller space than naively expected.

— Theory-agnostic nonclassicality certification in an integrated photonic circuit  (2609.18671 - Rossi et al., 16 Sep 2026) in Section 5, Conclusions