Mutual Unbiasedness in Coarse-grained Continuous Variables

Abstract

The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connection between discrete and continuous variable quantum mechanics.

5 pages, 3 figures + Supplemental Material (1 page) v2: Introduction expanded, minor typos corrected

References in corpus (43)

• On mutually unbiased bases
• Experimental high-dimensional two-photon entanglement and violations of generalised Bell inequalities
• Entropic Uncertainty Relations and their Applications
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• High-rate quantum cryptography in untrusted networks
• Generation and Confirmation of a (100x100)-dimensional entangled Quantum System
• EPR Steering Inequalities from Entropic Uncertainty Relations
• Quantum key distribution with higher-order alphabets using spatially-encoded qudits
• Entanglement detection via mutually unbiased bases
• High-Dimensional Single-Photon Quantum Gates: Concepts and Experiments
• Quantum Randomness Certified by the Uncertainty Principle
• Complementarity relations for quantum coherence
• Maximal Violation of Bell Inequalities using Continuous Variables Measurements
• High-dimensional decoy-state quantum key distribution over 0.3 km of multicore telecommunication optical fibers
• Full-field quantum correlations of spatially entangled photons
• Mutually unbiased measurements in finite dimensions
• Characterization of high-dimensional entangled systems via mutually unbiased measurements
• Violation of Continuous Variable EPR Steering with Discrete Measurements
• Universal steering inequalities
• Universal Quantum Computing with Arbitrary Continuous-Variable Encoding
• Scalable fiber integrated source for higher-dimensional path-entangled photonic quNits
• Optical Hybrid Quantum Information Processing
• Equilibrium to nonequilibrium condensation in driven-dissipative semiconductor systems
• Unbounded violation of quantum steering inequalities
• Quantum communication with photons
• Quantum process reconstruction based on mutually unbiased basis
• Cyclic transformation of orbital angular momentum modes
• Loss-tolerant EPR steering for arbitrary dimensional states: joint measurability and unbounded violations under losses
• Optimal Uncertainty Relations for Extremely Coarse-grained Measurements
• Reliable Entanglement Detection Under Coarse--Grained Measurements
• The Quantum Hilbert Hotel
• Mutually Unbiased Bases for Continuous Variables
• Large violation of Bell inequalities using both particle and wave measurements
• Detecting entanglement of continuous variables with three mutually unbiased bases
• Certainty relations, mutual entanglement and non-displacable manifolds
• Maximal CHSH violations with low efficiency photodetection and homodyne measurements
• Heisenberg Uncertainty Relation for Coarse-grained Observables
• Multipartite correlations in mutually unbiased bases
• Missing data outside the detector range: application to continuous variable entanglement verification and quantum cryptography
• Uncertainty relations for characteristic functions
• Tomography of Spatial Mode Detectors
• Uncertainty in the context of multislit interferometry
• Multi-slit interferometry and commuting functions of position and momentum

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• Uncertainty Relations for coarse-grained measurements: an overview
• Five open problems in quantum information
• Testing for entanglement with periodic coarse-graining
• One-Sided Device-Independent Random Number Generation Through Fiber Channels
• Steering-based randomness certification with squeezed states and homodyne measurements
• Mutually Unbiased Coarse-Grained Measurements of Two or More Phase-Space Variables
• Mutually Unbiased Measurements, Hadamard Matrices, and Superdense Coding
• Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts
• State-Agnostic Approach to Certifying Electron-Photon Entanglement in Electron Microscopy
• Violation of steering inequality for generalized equiangular measurements
• Periodic discretized continuous observables are neither continuous nor discrete
• Optical computing of quantum revivals