Structure of Quantum Theory

Local tomography is the axiom that the state of a bipartite system is uniquely determined by the statistics of product measurements. It is widely employed as a postulate in axiomatic reconstructions of quantum theory. For local tomography to be a physically meaningful property of quantum theory, it should be satisfied robustly: distinguishing quantum theory from any theory violating local tomography should not require infinite precision. We show that this robustness requirement fails by constructing a generalized probabilistic theory (GPT) that violates local tomography, yet no experiment with finite precision, however high, can distinguish it from quantum theory. In this sense, quantum theory almost fails to be locally tomographic. This lack of robustness calls into question the use of local tomography in reconstructions of quantum theory.

This talk is based on further developments of ideas presented in https://arxiv.org/abs/2601.18872.