Corrected Bell and Noncontextuality Inequalities for Realistic Experiments
arXiv:2310.19383 · doi:10.1098/rsta.2023.0011
Abstract
Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a nonclassical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden variables, for which it forces a contradiction with the assumptions of parameter-independence and determinism. The former can be justified by the empirical property of non-signalling or non-disturbance, and the latter by the empirical property of measurement sharpness. However, in realistic experiments neither empirical property holds exactly, which leads to possible objections to contextuality as a form of nonclassicality, and potential vulnerabilities for supposed quantum advantages. We introduce measures to quantify both properties, and introduce quantified relaxations of the corresponding assumptions. We prove the continuity of a known measure of contextuality, the contextual fraction, which ensures its robustness to noise. We then bound the extent to which these relaxations can account for contextuality, via corrections terms to the contextual fraction (or to any noncontextuality inequality), culminating in a notion of genuine contextuality, which is robust to experimental imperfections. We then show that our result is general enough to apply or relate to a variety of established results and experimental setups.
arXiv commentv2: accepted for publication in PTRSA; 20 pages + 14 pages of appendices, 3 figures
References in corpus (51)
- Hidden Variables and the Two Theorems of John Bell
- Contextuality for preparations, transformations, and unsharp measurements
- Contextuality supplies the magic for quantum computation
- A simple test for hidden variables in spin-1 system
- The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
- State-independent experimental test of quantum contextuality
- Graph-Theoretic Approach to Quantum Correlations
- Is the quantum state real? An extended review of -ontology theorems
- Experimental non-classicality of an indivisible quantum system
- Contextuality in Measurement-based Quantum Computation
- Maximally Non-Local and Monogamous Quantum Correlations
- Preparation contextuality powers parity-oblivious multiplexing
- A Combinatorial Approach to Nonlocality and Contextuality
- Relaxed Bell inequalities and Kochen-Specker theorems
- All noncontextuality inequalities for the n-cycle scenario
- The contextual fraction as a measure of contextuality
- Contextuality as a resource for models of quantum computation on qubits
- Entropy accumulation
- Compatibility and noncontextuality for sequential measurements
- Necessary and Sufficient Conditions for Extended Noncontextuality in a Broad Class of Quantum Mechanical Systems
- True Contextuality Beats Direct Influences in Human Decision Making
- From the Kochen-Specker theorem to noncontextuality inequalities without assuming determinism
- Necessary and sufficient conditions for macroscopic realism from quantum mechanics
- Asymptotically optimal data analysis for rejecting local realism
- Memory cost of quantum contextuality
- The status of determinism in proofs of the impossibility of a noncontextual model of quantum theory
- Experimental fully contextual correlations
- Device-independent point estimation from finite data and its application to device-independent property estimation
- Efficient quantification of experimental evidence against local realism
- Quantum Advantage from Sequential-Transformation Contextuality
- Device-Independent Randomness Generation in the Presence of Weak Cross-Talk
- Bell Locality and the Nonlocal Character of Nature
- What does an experimental test of quantum contextuality prove or disprove?
- Significant-loophole-free test of Kochen-Specker contextuality using two species of atomic-ions
- Experimental observation of Hardy-like quantum contextuality
- Axiomatic approach to contextuality and nonlocality
- Measures of Contextuality and Noncontextuality
- From statistical proofs of the Kochen-Specker theorem to noise-robust noncontextuality inequalities
- Measurement sharpness cuts nonlocality and contextuality in every physical theory
- Proposal of a two-qutrit contextuality test free of the finite precision and compatibility loopholes
- Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
- Quantifying quantum invasiveness
- Contextuality bounds the efficiency of classical simulation of quantum processes
- The Quantum Monad on Relational Structures
- Certified randomness in tight space
- Contextuality and inductive bias in quantum machine learning
- Towards a complete cohomology invariant for non-locality and contextuality
- On the Quantum-like Contextuality of Ambiguous Phrases
- On geometrical aspects of the graph approach to contextuality
- A note on the relation between the Contextual Fraction and CNT2
- Measures of contextuality in cyclic systems and the negative probabilities measure CNT3