A simple test for hidden variables in spin-1 system

Abstract

We resolve an old problem about the existence of hidden parameters in a three-dimensional quantum system by constructing an appropriate Bell's type inequality. This reveals a nonclassical nature of most spin-$1$ states. We shortly discuss some physical implications and an underlying cause of this nonclassical behavior, as well as a perspective of its experimental verification.

4 pages, 1 figure

References in corpus (11)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Hidden Variables and the Two Theorems of John Bell
• On the role of entanglement in quantum computational speed-up
• Research on Hidden Variable Theories: a review of recent progresses
• Manipulating biphotonic qutrits
• Generalizations of entanglement based on coherent states and convex sets
• Qutrit state engineering with biphotons
• Experiments towards Falsification of Noncontextual Hidden Variable Theories
• Bell's inequality for a single spin 1/2 particle and quantum contextuality
• Orthogonality of Biphoton Polarization States

Cited by in corpus (308)

• Multi-photon entanglement and interferometry
• Quantum Random Number Generators
• Qudits and high-dimensional quantum computing
• Experimentally testable state-independent quantum contextuality
• Multi-photon entanglement in high dimensions
• Self-testing of quantum systems: a review
• Graph-Theoretic Approach to Quantum Correlations
• Is the quantum state real? An extended review of $\psi$-ontology theorems
• Experimental non-classicality of an indivisible quantum system
• Specker's Parable of the Over-protective Seer: A Road to Contextuality, Nonlocality and Complementarity (PLUS AN ERRATUM)
• State-independent proof of Kochen-Specker theorem with 13 rays
• An experimental test of noncontextuality without unwarranted idealizations
• Kochen-Specker Contextuality
• A Combinatorial Approach to Nonlocality and Contextuality
• Simple explanation of the quantum violation of a fundamental inequality
• All noncontextuality inequalities for the n-cycle scenario
• Three addressable spin qubits in a molecular single-ion magnet
• Computational speed-up with a single qudit
• Computational speed-up in a single qudit NMR quantum information processor
• An entropic approach to local realism and noncontextuality
• Quantifying Contextuality
• Bounding temporal quantum correlations
• Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing
• Testing foundations of quantum mechanics with photons
• Bounding the quantum dimension with contextuality
• Compatibility and noncontextuality for sequential measurements
• Necessary and Sufficient Conditions for Extended Noncontextuality in a Broad Class of Quantum Mechanical Systems
• Entropic Inequalities and Marginal Problems
• State-independent experimental tests of quantum contextuality in a three dimensional system
• Entropic Test of Quantum Contextuality
• Generalized monogamy of contextual inequalities from the no-disturbance principle
• Entanglement: Quantum or Classical?
• Optimal inequalities for state-independent contextuality
• Fundamental monogamy relation between contextuality and nonlocality
• State-independent experimental test of quantum contextuality in an indivisible system
• Is there contextuality in behavioral and social systems?
• A Kochen-Specker inequality from a SIC
• Simple Hardy-like proof of quantum contextuality
• Quantum Correlations are Tightly Bound by the Exclusivity Principle
• Simple method for experimentally testing any form of quantum contextuality
• Robust self-testing of quantum systems via noncontextuality inequalities
• Contextuality without nonlocality in a superconducting quantum system
• Sustained state-independent quantum contextual correlations from a single ion
• All the noncontextuality inequalities for arbitrary prepare-and-measure experiments with respect to any fixed sets of operational equivalences
• Contextuality in Three Types of Quantum-Mechanical Systems
• Necessary and sufficient condition for quantum state-independent contextuality
• The exclusivity principle forbids sets of correlations larger than the quantum set
• Quantum contextuality provides communication complexity advantage
• Basic exclusivity graphs in quantum correlations
• Optimal quantum preparation contextuality in $n$-bit parity-oblivious multiplexing task
• Properties and Applications of the Kirkwood-Dirac Distribution
• Proof of a Conjecture on Contextuality in Cyclic Systems with Binary Variables
• Converting contextuality into nonlocality
• Entropic inequalities as a necessary and sufficient condition to noncontextuality and locality
• Proofs of the Kochen-Specker theorem based on a system of three qubits
• What does an experimental test of quantum contextuality prove or disprove?
• Robust preparation noncontextuality inequalities in the simplest scenario
• Noncontextual wirings
• Finite tight frames and some applications
• Leggett-Garg macrorealism and the quantum nondisturbance conditions
• Significant-loophole-free test of Kochen-Specker contextuality using two species of atomic-ions
• Experimental observation of Hardy-like quantum contextuality
• Optimal classical simulation of state-independent quantum contextuality
• Concentration phenomena in the geometry of Bell correlations
• Axiomatic approach to contextuality and nonlocality
• Necessary and sufficient condition for contextuality from incompatibility
• Bell inequalities for the simplest exclusivity graph
• Pentagrams and paradoxes
• Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality
• Probabilistic Foundations of Contextuality
• Practically state-independent test of contextuality with 9 observables
• Synchronous observation of Bell nonlocality and state-dependent Kochen-Specker contextuality
• From statistical proofs of the Kochen-Specker theorem to noise-robust noncontextuality inequalities
• Necessary and sufficient conditions for state-independent measurement contextual scenarios
• Classical Physics and the Bounds of Quantum Correlations
• Proofs of the Kochen-Specker theorem based on the N-qubit Pauli group
• Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces
• A dimensionality and purity measure for high-dimensional entangled states
• Violations of locality and free choice are equivalent resources in Bell experiments
• Classical causal models for Bell and Kochen-Specker inequality violations require fine-tuning
• Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden variable theories
• Unified approach to contextuality, non-locality, and temporal correlations
• Contextuality in phase space
• Quantum key distribution protocol based on contextuality monogamy
• Experimental generalized contextuality with single-photon qubits
• Rotational covariance and GHZ contradictions for three or more particles of any dimension
• Contextuality and Noncontextuality Measures and Generalized Bell Inequalities for Cyclic Systems
• Contextuality and nonlocality in 'no signaling' theories
• Experimental Test of the Quantum Violation of the Noncontextuality Inequalities for the n-Cycle Scenario
• Quantum correlations from simple assumptions
• Minimal state-dependent proof of measurement contextuality for a qubit
• Proof of the Peres conjecture for contextuality
• Parity proofs of the Kochen-Specker theorem based on 60 complex rays in four dimensions
• Experimental test of contextuality in quantum and classical systems
• Multigraph approach to quantum non-locality
• Leggett-Garg Macrorealism and temporal correlations
• Contextuality in entanglement-assisted one-shot classical communication
• Quantum information
• Quantum Contextuality with Stabilizer States
• Errors in quantum tomography: diagnosing systematic versus statistical errors
• Quantum Contextuality
• Probing the limits of correlations in an indivisible quantum system
• No-Forcing and No-Matching Theorems for Classical Probability Applied to Quantum Mechanics
• Contextuality Analysis of the Double Slit Experiment (With a Glimpse Into Three Slits)
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• Contextuality-by-Default description of Bell tests: Contextuality as the rule not as an exception
• Experimentally Probing the Algorithmic Randomness and Incomputability of Quantum Randomness
• Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8
• Bell inequalities from variable elimination methods
• Twin inequality for fully contextual quantum correlations
• On generalized entropies and information-theoretic Bell inequalities under decoherence
• Specker's fundamental principle of quantum mechanics
• Inequalities witnessing coherence, nonlocality, and contextuality
• Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices
• Randomness expansion secured by quantum contextuality
• Contextuality in spin-orbit laser modes
• Gadget structures in proofs of the Kochen-Specker theorem
• Quantum theory realises all joint measurability graphs
• Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres
• Tests against noncontextual models with measurement disturbances
• Activation of monogamy in non-locality using local contextuality
• Contextuality, Coherences, and Quantum Cheshire Cats
• Noncontextuality Inequalities from Antidistinguishability
• What makes quantum clicks special?
• Graph-theoretic strengths of contextuality
• Conditions for monogamy of quantum correlations in multipartite systems
• Contextuality and The Single-Qubit Stabilizer Formalism
• The complete Heyting algebra of subsystems and contextuality
• Coherence makes quantum systems 'magical'
• Experimental demonstration of quantum contextuality on an NMR qutrit
• Device-independent quantification of measurement incompatibility
• On the violation of L$\ddot{u}$ders bound of macrorealist and noncontextual inequalities
• Realization of a binary-outcome projection measurement of a three-level superconducting quantum system
• Does ignorance of the whole imply ignorance of the parts? - Large violations of non-contextuality in quantum theory
• Classical causal models cannot faithfully explain Bell nonlocality or Kochen-Specker contextuality in arbitrary scenarios
• On Joint Distributions, Counterfactual Values, and Hidden Variables in Relation to Contextuality
• Extensions of Hardy-type true-implies-false gadgets to classically obtain indistinguishability
• Unification of Bell, Leggett-Garg and Kochen-Specker inequalities: A hybrid spatio-temporal inequality
• Testing noncontextuality inequalities that are building blocks of quantum correlations
• Self-testing of binary Pauli measurements requiring neither entanglement nor any dimensional restriction
• Canonical Leggett-Garg Inequality: Nonclassicality of temporal quantum correlations under energy constraint
• Separability and entanglement of the qudit X-state with j = 3/2
• Monogamy Relation in No-disturbance Theories
• A proof of the Kochen-Specker theorem can always be converted to a state-independent noncontextuality inequality
• New forms of quantum value indefiniteness suggest that incompatible views on contexts are epistemic
• Bell non-locality and Kochen-Specker contextuality: How are they connected?
• Reformulating noncontextuality inequalities in an operational approach
• Monogamy inequality for entanglement and local contextuality
• Faithful orthogonal representations of graphs from partition logics
• Coexistence of Kochen-Specker inequalities and noncontextuality inequalities
• The magic of universal quantum computing with permutations
• Geometry of Uncertainty Relations for Linear Combinations of Position and Momentum
• Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem
• The Problem of Contextuality and the Impossibility of Experimental Metaphysics Thereof
• Topological contextuality and anyonic statistics of photonic-encoded parafermions
• Simulating extremal temporal correlations
• Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem
• Benchmarks of Nonclassicality for Qubit Arrays
• Formulation of Leggett-Garg inequalities in terms of $q$-entropies
• Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem
• Experimental demonstration of the connection between quantum contextuality and graph theory
• Breakdown of the classical description of a local system
• Primitive Nonclassical Structures of the $N$-qubit Pauli Group
• Contextuality in Quantum Mechanics: Testing the Klyachko Inequality
• Hypergraph Contextuality
• Contextuality beyond the Kochen-Specker theorem
• Quantum contextuality from a simple principle?
• Advanced Analysis of Quantum Contextuality in a Psychophysical Double-Detection Experiment
• Mutually Unbiased Bases and Complementary Spin 1 Observables
• Certifying dimension of quantum systems by sequential projective measurements
• Experimental test of high-dimensional quantum contextuality based on contextuality concentration
• On Possibilistic Conditions to Contextuality and Nonlocality
• Optimal and tight Bell inequalities for state-independent contextuality sets
• Universal security for randomness expansion from the spot-checking protocol
• Geometry of joint reality: device-independent steering and operational completeness
• Experimental demonstration of fully contextual quantum correlations on an NMR quantum information processor
• Bounding quantum theory with the exclusivity principle in a two-city experiment
• Contextuality under weak assumptions
• Quantum violation of entropic non-contextual inequality in four-dimension
• Contextuality of Identical Particles
• Roots and (re)sources of value (in)definiteness versus contextuality. A contribution to the Pitowsky Volume in memory of Itamar Pitowsky (1950--2010)
• Quantum correlations expressed as information and entropic inequalities for composite and noncomposite systems
• On the tightness of correlation inequalities with no quantum violation
• Local certification of programmable quantum devices of arbitrary high dimensionality
• Corrected Bell and Noncontextuality Inequalities for Realistic Experiments
• Sequential propagation of a single photon through five measurement contexts in a three-path interferometer
• Logical and inequality based contextuality for qudits
• Demonstrating quantum contextuality of indistinguishable particles by a single family of noncontextuality inequalities
• Contextuality in bosonic bunching
• An experimental proposal for revealing contextuality in almost all qutrit states
• State-independent quantum contextuality with projectors of nonunit rank
• Semi-device independent randomness certification using Mermin's proof of Kochen-Specker contextuality
• The Exclusivity Principle and the Set of Quantum Correlations
• The rank of contextuality
• Measurement Contextuality and Planck's Constant
• Entropic No-Disturbance as a Physical Principle
• Large violations in Kochen Specker contextuality and their applications
• Quantum realism and quantum surrealism
• Hierarchical axioms for quantum mechanics
• Separability and entanglement of spin $1$ particle
• Contextuality witness inspired by optimal state discrimination
• On the origin of nonclassicality in single systems
• Kenfack Zyczkowski indicator of nonclassicality for two non-equivalent representations of Wigner function of qutrit
• Simple state preparation for contextuality tests with few observables
• Characterizing quantum correlations in the nonsignaling framework
• The Degree of Quantum Contextuality in terms of Concurrence for the KCBS Scenario
• Revealing quantum contextuality using a single measurement device
• Quantum sets of the multicolored-graph approach to contextuality
• Experimental Realization of Quantum Violation of Entropic Noncontextual Inequality in Four Dimension Using IBM Quantum Computer
• The Golay codes and Quantum Contextuality
• Classical Limits and Contextuality in a Scenario of Multiple Observers
• Varieties of contextuality based on probability and structural nonembeddability
• State-recycling method for testing contextuality
• Construction of State-independent Proofs for Quantum Contextuality
• Violating the KCBS inequality with a toy mechanism
• N term pairwise correlation inequalities, steering and joint measurability
• A State-Dependent Noncontextuality Inequality in Algebraic Quantum Theory
• The Effect of Decoherence on the Contextual and Nonlocal Properties of a Biphoton
• Quantum contextuality for rational vectors
• Non-classical Correlations in n-Cycle Setting
• The problem of quantum correlations and the totalitarian principle
• A Logical Proof of Quantum Correlations Requiring Entanglement Measurements
• Context-independent mapping and free choice are equivalent
• Quantum contextuality for a three-level system sans realist model
• Epistemic Odds of Contextuality in Cyclic Systems
• Generalised Kochen-Specker Theorem for Finite Non-Deterministic Outcome Assignments
• Quantum mechanical effect of path-polarization contextuality for a single photon
• Extended Wigner's friend paradoxes do not require nonlocal correlations
• Non-Kochen-Specker Contextuality
• Nonclassical oscillations in pre- and post-selected quantum walks
• Experimental demonstration of the violation of the temporal Peres-Mermin inequality using contextual temporal correlations and noninvasive measurements
• Quantum violation of the Suppes-Zanotti inequalities and "contextuality"
• Bosonic Indistinguishability-Dependent Contextuality
• Optimal Measurement Structures for Contextuality Applications
• The many mathematical faces of Mermin's proof of the Kochen-Specker theorem
• A computational test of quantum contextuality, and even simpler proofs of quantumness
• Lifting noncontextuality inequalities
• Experimental Test of Contextuality based on State Discrimination with a Single Qubit
• Tracing quantum correlations back to collective interferences
• The relation between nonlocality and contextuality for a biphoton
• Wigner and friends, a map is not the territory! Contextuality in multi-agent paradoxes
• Super quantum probabilities and three-slit experiments -- Wright's pentagon state and the Popescu-Rohrlich box require third-order interference
• Contextuality and Nonlocality in Decaying Multipartite Systems
• Monogamy relations of entropic non-contextual inequalities and their experimental realization
• Steering in spin tomographic probability representation
• Experimentally ruling out joint reality based on operational completeness
• Role of nonclassical temporal correlation in powering quantum random access codes
• No contextual advantage in non-paradoxical scenarios of two state vector formalism
• Exploring the boundary of quantum correlations with a time-domain optical processor
• Reexamination of the Kochen-Specker theorem: Relaxation of the completeness assumption
• Characterizing high-dimensional quantum contextuality
• Quantum contextuality of complementary photon polarizations explored by adaptive input state control
• Connecting extended Wigner's friend arguments and noncontextuality
• Bell inequality violations under reasonable and under weak hypotheses
• Contextuality of Quantum Error-Correcting Codes
• Harvesting Contextuality from the Vacuum
• Statistical signatures of quantum contextuality
• Exclusivity principle and unphysicality of Garg-Mermin correlation
• States Violating Both Locality and Noncontextuality Inequalities in Quantum Theory
• An explicit contextualized hidden variable model replicating an indivisible quantum system
• Twenty years of quantum contextuality at USTC
• Interrelation of nonclassicality conditions through stabiliser group homomorphism
• Trade-off relations between Bell nonlocality and local Kochen-Specker contextuality in generalized Bell scenarios
• Atom graph, partial Boolean algebra and quantum contextuality
• Unexpected consequences of Post-Quantum theories in the graph-theoretical approach to correlations
• Chromatic Quantum Contextuality
• Independence and totalness of subspaces in phase space methods
• Contextuality and dichotomizations of random variables
• Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions
• Demonstration of universal contextuality through communication games free of both operational inequivalence and compatibility loopholes
• Three-Qubit-Embedded Split Cayley Hexagon is Contextuality Sensitive
• Experimental Approach to Demonstrating Contextuality for Qudits
• Quantum contextuality of a qutrit state
• Graph-theoretic approach to dimension witnessing
• Contextuality, Witness of Quantum Weirdness
• The unspeakable why
• Insights into Quantum Contextuality and Bell Nonclassicality: A Study on Random Pure Two-Qubit Systems
• Classical Invasive Description of Informationally-Complete Quantum Processes
• Nonclassicality of induced coherence witnessed by contextuality
• A principle of quantumness
• Multisetting Bell inequalities for $N$ spins-1 avoiding KS contradiction
• Graph theoretic quantum contextuality and unextendible Product Bases
• Analogs of absolutely maximally entangled states in nonlocal correlations via the sheaf-theoretic framework and its applications
• Bell Meets General Philosophers of Science : Reassessing Measurement Independence
• Quantum Random Number Generator based on Violations of the Free CHSH-3 Inequality
• Disproving hidden variable models with spin magnitude conservation
• A Quantum Gödelian Hunch
• Contextuality, superlocality and nonclassicality of supernoncontextuality
• Accounting for gauge symmetries in CHSH experiments
• Spin Squeezing, Macrorealism and the Heisenberg uncertainty principle
• Differentiability of correlations in Realistic Quantum Mechanics
• A QBist Ontology
• On random classical marginal problems with applications to quantum information theory
• Indistinguishability and Negative Probabilities
• Exploring Quantum Contextuality with the Quantum Moebius-Escher-Penrose hypergraph
• All fundamental non-contextuality inequalities are unique
• The Partition Formalism and New Entropic-Information Inequalities for Real Numbers on an Example of Clebsch-Gordan Coefficients
• Simultaneous All-versus-Nothing Refutation of Local Realism and Noncontextuality by a Single System
• State-independent experimental test of quantum contextuality in solid state system
• Inequalities for purity parameters for multipartite and single qudit states
• Quantum correlations in composite systems under global unitary operations
• Hidden variable problem for a family of continuously many spin 1 measurements
• Revealing universal quantum contextuality through communication games
• Probe of Generic Quantum Contextuality and Nonlocal Resources for Qubits
• Quantum coherence and negative quasi probabilities in a contextual three-path interferometer
• Quantum contextuality from measurement invasiveness
• Retrit States Violating the KCBS Inequality and Necessary Conditions for Maximal Contextuality
• Investigating Bell Inequalities for Multidimensional Relevance Judgments in Information Retrieval