Contextuality without access to a tomographically complete set

Abstract

The non-classicality of single quantum systems can be formalised using the notion of contextuality. But can contextuality be convincingly demonstrated in an experiment, without reference to the quantum formalism? The operational approach to contextuality due to Spekkens requires finding operationally equivalent preparation procedures. Previously these have been obtained by demanding indistinguishability under a set of measurements taken to be tomographically complete. In the language of generalised probability theories, this requires the ability to explore all the dimensions of the system's state space. However, if the true tomographically complete set is larger than the set assumed, the extra measurements could break the operational equivalences and hence eliminate the putative contextuality. Such extra dimensions could arise in post-quantum theories, but even if quantum theory is exact there can be unexpected degrees of freedoms due to imperfections in an experiment. Here we design tests of contextuality that are immune to this effect for a given number of extra measurements in the tomographically complete set, even if nothing is known about their statistics. This allows contextuality to be demonstrated with weaker assumptions.

14+3 pages, 3+1 figures. Preliminary version, comments welcome

References in corpus (10)

• Contextuality for preparations, transformations, and unsharp measurements
• Quantum Theory From Five Reasonable Axioms
• Device-independent tests of classical and quantum dimensions
• An experimental test of noncontextuality without unwarranted idealizations
• Certifying the dimension of classical and quantum systems in a prepare-and-measure scenario with independent devices
• All the noncontextuality inequalities for arbitrary prepare-and-measure experiments with respect to any fixed sets of operational equivalences
• Random 'choices' and the locality loophole
• Representing probabilistic data via ontological models
• Contextuality bounds the efficiency of classical simulation of quantum processes
• Information processing in generalized probabilistic theories

Cited by in corpus (3)

• Uniqueness of noncontextual models for stabilizer subtheories
• Contextual advantage for state-dependent cloning
• Contextuality in entanglement-assisted one-shot classical communication