Contextuality in phase space

Abstract

We present a general framework for contextuality tests in phase space using displacement operators. First, we derive a general condition that a single-mode displacement operator should fulfill in order to construct Peres-Mermin square and similar scenarios. This approach offers a straightforward scheme for experimental implementations of the tests via modular variable measurements. In addition to the continuous variable case, our condition can also be applied to finite-dimensional systems in discrete phase space, using Heisenberg-Weyl operators. This approach, therefore, offers a unified picture of contextuality with a geometric flavor.

5+3 pages, 4 figures. Missing appendix added

References in corpus (30)

• Contextuality supplies the magic for quantum computation
• A simple test for hidden variables in spin-1 system
• Experimentally testable state-independent quantum contextuality
• Strong magnetic coupling between an electronic spin qubit and a mechanical resonator
• State-independent experimental test of quantum contextuality
• Nonlocality of Einstein-Podolsky-Rosen State in Wigner Representation
• Ion-trap quantum logic using long-wavelength radiation
• Experimental non-classicality of an indivisible quantum system
• Contextuality in Measurement-based Quantum Computation
• State-independent proof of Kochen-Specker theorem with 13 rays
• State-independent quantum contextuality with single photons
• Testing contextuality on quantum ensembles with one clean qubit
• Spin-dependent forces on trapped ions for phase-stable quantum gates and motional Schrodinger-cat states
• Wigner function negativity and contextuality in quantum computation on rebits
• Universality of state-independent violation of correlation inequalities for noncontextual theories
• Compatibility and noncontextuality for sequential measurements
• Bounding the quantum dimension with contextuality
• State-independent experimental tests of quantum contextuality in a three dimensional system
• Probing macroscopic realism via Ramsey correlations measurements
• Optimal inequalities for state-independent contextuality
• Applying the simplest Kochen-Specker set for quantum information processing
• Greenberger-Horne-Zeilinger paradox for continuous variables
• Necessary and sufficient condition for quantum state-independent contextuality
• Detecting entanglement in spatial interference
• Necessary and sufficient conditions for state-independent measurement contextual scenarios
• State-independent quantum contextuality for continuous variables
• Generation of spin-motion entanglement in a trapped ion using long-wavelength radiation
• Simple explanation of the quantum limits of genuine $n$-body nonlocality
• Detecting and estimating continuous-variable entanglement by local orthogonal observables
• Tests against noncontextual models with measurement disturbances

Cited by in corpus (24)

• Kochen-Specker Contextuality
• Direct characteristic-function tomography of quantum states of the trapped-ion motional oscillator
• Sequential modular position and momentum measurements of a trapped ion mechanical oscillator
• Heisenberg-Weyl Observables: Bloch vectors in phase space
• Quantum information processing in phase space: A modular variables approach
• Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements
• Quantum Contextuality
• Uncertainty Relations for coarse-grained measurements: an overview
• Qudit Hypergraph States
• Proposal for a macroscopic test of local realism with phase-space measurements
• Geometry of Uncertainty Relations for Linear Combinations of Position and Momentum
• General conditions for maximal violation of non-contextuality in discrete and continuous variables
• Separability criteria based on Heisenberg-Weyl representation of density matrices
• No-broadcasting characterizes operational contextuality
• Continuous-variable nonlocality and contextuality
• Wigner distribution on a double cylinder phase space for studying quantum error correction protocol
• Separability criteria based on the Weyl operators
• Bloch sphere analog of qudits using Heisenberg-Weyl Operators
• Noise-adaptive test of quantum correlations with quasiprobability functions
• Periodic discretized continuous observables are neither continuous nor discrete
• Bosonic fields in states with undefined particle numbers possess detectable non-contextuality features, plus more
• Differential Geometry of Contextuality
• The Interplay between Quantum Contextuality and Wigner Negativity
• Arbitrarily large violations of non-contextuality in single mode photon states with positive Wigner function