Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs
arXiv:2409.13024 · doi:10.22331/q-2025-10-13-1880
Abstract
It is commonly believed that failures of tomographic completeness undermine assessments of nonclassicality in noncontextuality experiments. In this work, we study how such failures can indeed lead to mistaken assessments of nonclassicality. We then show that proofs of the failure of noncontextuality are robust to a very broad class of failures of tomographic completeness, including the kinds of failures that are likely to occur in real experiments. We do so by showing that such proofs actually rely on a much weaker assumption that we term relative tomographic completeness: namely, that one's experimental procedures are tomographic for each other. Thus, the failure of noncontextuality can be established even with coarse-grained, effective, emergent, or virtual degrees of freedom. This also implies that the existence of a deeper theory of nature (beyond that being probed in one's experiment) does not in and of itself pose any challenge to proofs of nonclassicality. To prove these results, we first introduce a number of useful new concepts within the framework of generalized probabilistic theories (GPTs). Most notably, we introduce the notion of a GPT subsystem, generalizing a range of preexisting notions of subsystems (including those arising from tensor products, direct sums, decoherence processes, virtual encodings, and more). We also introduce the notion of a shadow of a GPT fragment, which captures the information lost when one's states and effects are unknowingly not tomographic for one another.
31 pages plus appendices; Many figures and diagrams
References in corpus (54)
- Reference frames, superselection rules, and quantum information
- Contextuality for preparations, transformations, and unsharp measurements
- Probabilistic theories with purification
- Virtual Quantum Subsystems
- A derivation of quantum theory from physical requirements
- Negativity and contextuality are equivalent notions of nonclassicality
- Decoherence-Free Subspaces and Subsystems
- Anomalous Weak Values Are Proofs of Contextuality
- An experimental test of noncontextuality without unwarranted idealizations
- Preparation contextuality powers parity-oblivious multiplexing
- Contextual advantage for state discrimination
- General probabilistic theories: An introduction
- Anomalous weak values and contextuality: robustness, tightness, and imaginary parts
- From the Kochen-Specker theorem to noncontextuality inequalities without assuming determinism
- Certifying quantum signatures in thermodynamics and metrology via contextuality of quantum linear response
- Generalized Probabilistic Theories Without the No-Restriction Hypothesis
- Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics
- The Characterization of Noncontextuality in the Framework of Generalized Probabilistic Theories
- State independent contextuality advances one-way communication
- Quartic quantum theory: an extension of the standard quantum mechanics
- Measurement incompatibility and steering are necessary and sufficient for operational contextuality
- Why interference phenomena do not capture the essence of quantum theory
- Experimentally bounding deviations from quantum theory in the landscape of generalized probabilistic theories
- Uniqueness of noncontextual models for stabilizer subtheories
- Communication games reveal preparation contextuality
- Contextual advantage for state-dependent cloning
- Contextual advantages and certification for maximum confidence discrimination
- Aspects of the phenomenology of interference that are genuinely nonclassical
- Entanglement is necessary for emergent classicality in all physical theories
- Entanglement is an inevitable feature of any non-classical theory
- What is nonclassical about uncertainty relations?
- From statistical proofs of the Kochen-Specker theorem to noise-robust noncontextuality inequalities
- Contextuality without incompatibility
- Contextuality in entanglement-assisted one-shot classical communication
- A structure theorem for generalized-noncontextual ontological models
- Coherence and contextuality in a Mach-Zehnder interferometer
- An invertible map between Bell non-local and contextuality scenarios
- Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
- Almost Quantum Correlations are Inconsistent with Specker's Principle
- Discriminating mirror symmetric states with restricted contextual advantage
- Experimentally bounding deviations from quantum theory for a photonic three-level system using theory-agnostic tomography
- Fine's theorem, noncontextuality, and correlations in Specker's scenario
- Solvable Criterion for the Contextuality of any Prepare-and-Measure Scenario
- A linear program for testing nonclassicality and an open-source implementation
- Contextuality with vanishing coherence and maximal robustness to dephasing
- Agents, subsystems, and the conservation of information
- Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem
- Testing quantum theory by generalizing noncontextuality
- A review and reformulation of macroscopic realism: resolving its deficiencies using the framework of generalized probabilistic theories
- Operational locality in global theories
- Contextuality in anomalous heat flow
- No-broadcasting characterizes operational contextuality
- Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks
- Hyper-decoherence in Density Hypercubes