Contextuality, superlocality and nonclassicality of supernoncontextuality

Abstract

Contextuality is a fundamental manifestation of nonclassicality, indicating that for certain quantum correlations, sets of jointly measurable variables cannot be pre-assigned values independently of the measurement context. In this work, we characterize nonclassical quantum correlation beyond contextuality, in terms of supernoncontextuality, namely the higher-than-quantum hidden-variable(HV) dimensionality required to reproduce the given noncontextual quantum correlations. Thus supernoncontextuality is the contextuality analogue of superlocality. Specifically, we study the quantum system of two-qubit states in a scenario composed of five contexts that demonstrate contextuality in a state-dependent fashion. For this purpose, we use the framework of boxes, whose behavior is described by a set of probabilities satisfying the no-disturbance conditions. We first demonstrate that while superlocality is necessary to observe a contextual box, superlocality is not sufficient for contextuality. On the other hand, a noncontextual superlocal box can be supernoncontextual, but superlocality is not a necessary condition. We then introduce a notion of nonclassicality beyond the standard contextuality, called semi-device-independent contextuality. We study semi-device-independent contextuality of two-qubit states in the above mentioned scenario and demonstrate how supernoncontextuality implies this nonclassicality. To this end, we propose a criterion and a measure of semi-device-independent contextuality.

v2 (submitted to another journal): error in "which range noisy Peres box contextual" corrected- nonclassicality based on supernoncontextuality termed as "semi-device-independent contextuality"- a criterion and quantification of semi-device-independent contextuality studied - removed contents related to information-theoretic measures of simultaneous correlations in MUBs. 16 pages

References in corpus (48)

• Introducing Quantum Discord
• Bell nonlocality
• Classical, quantum and total correlations
• Device-independent security of quantum cryptography against collective attacks
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Random Numbers Certified by Bell's Theorem
• No Signalling and Quantum Key Distribution
• From Bell's Theorem to Secure Quantum Key Distribution
• Contextuality supplies the magic for quantum computation
• Quantum Steering
• A simple test for hidden variables in spin-1 system
• Experimentally testable state-independent quantum contextuality
• The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
• State-independent experimental test of quantum contextuality
• Self-testing of quantum systems: a review
• Certified randomness in quantum physics
• State-independent quantum contextuality with single photons
• Kochen-Specker Contextuality
• Computational power of correlations
• 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
• Quantifying Contextuality
• Entanglement assisted random access codes
• Proposed experiment for testing quantum contextuality with neutrons
• Certifying the building blocks of quantum computers from Bell's theorem
• State independent contextuality advances one-way communication
• Experimental fully contextual correlations
• Robust self-testing of quantum systems via noncontextuality inequalities
• Hybrid ququart-encoded quantum cryptography protected by Kochen-Specker contextuality
• Identifying Nonconvexity in the Sets of Limited-Dimension Quantum Correlations
• Bound non-locality and activation
• Noncontextual wirings
• Necessary and sufficient condition for contextuality from incompatibility
• Spatial versus Sequential Correlations for Random Access Coding
• Measurement-based classical computation
• Measurement-device-independent quantification of entanglement for given Hilbert space dimension
• Quantum key distribution protocol based on contextuality monogamy
• When Are Popescu-Rohrlich Boxes and Random Access Codes Equivalent?
• Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices
• Certified Quantum Measurement of Majorana Fermions
• Classical extension of quantum-correlated separable states
• Nonclassicality of local bipartite correlations
• Operational characterization of quantumness of unsteerable bipartite states
• Superunsteerability as a quantifiable resource for random access codes assisted by Bell-diagonal states
• Operational nonclassicality of local multipartite correlations in the limited-dimensional simulation scenario
• Asymmetric One-Sided Semi-Device-Independent Steerability of Quantum Discordant States
• Certification of two-qubit quantum systems with temporal inequality