Spatio-temporal quantum steering provides a framework for benchmarking the nonclassicality of general quantum state transfer processes. A central diagnostic is the no-signaling-in-time (NSIT) condition, whose violation can indicate basis-dependent hardware errors. However, finite measurement statistics may also yield apparent violations, thereby obscuring the detection of basis-dependent hardware errors. To address this, we construct a statistical hypothesis test under the null hypothesis that NSIT violations arise solely from statistical fluctuations. Combining the statistical properties of NSIT violation under the null hypothesis with Chebyshev's inequality, we obtain a distribution-free upper bound on the
p-value without parametric assumptions. We apply this method to two examples. For a single-qubit state-transfer experiment on a superconducting processor, we observe several instances that the NSIT violation is observed and the null hypothesis is simultaneously rejected by a small
p-value, providing statistical evidence of basis-dependent hardware errors. For a seven-qubit Hayden-Preskill teleportation protocol on IonQ devices, the null hypothesis is also rejected even when the average fidelity exceeds the classical threshold, while the associated nonclassicality measure vanishes. Our results highlight the necessity of statistical hypothesis testing for detecting basis-dependent errors in near-term quantum devices.
Bell [Helv. Phys.Act. 48 1975] described an idealized test of the projection postulate in order to illustrate the ambiguities in the experimental predictions of quantum theory. An approach to the implementation of such tests is outlined here, based on the interesting logical relationship between the projection postulate and the no-superluminal-signaling principle. Gisin's theorem [Helv. Phys. Act. 62 1989] shows that the no-signaling principle implies that any description of projection at the elementary level must be nondeterministic. The lack of determinism means that information cannot be instantiated in a reproducible and transmittable form in isolated microsystems. The implied limitation on information allows one to interpret the no-signaling principle in purely physical terms as a prohibition of superluminal information transmission. This prohibition, in turn, imposes tight constraints on the connection between projection and elementary processes, leading to a specific hypothesis about how projection effects originate. The hypothesis serves as the basis for the experimental proposal.