Reliable Entanglement Detection Under Coarse--Grained Measurements

Abstract

We derive reliable entanglement witnesses for coarse--grained measurements on continuous variable systems. These witnesses never return a "false positive" for identification of entanglement, under any degree of coarse graining. We show that, even in the case of Gaussian states, entanglement witnesses based on the Shannon entropy can outperform those based on variances. We apply our results to experimental identification of spatial entanglement of photon pairs.

Dedicated to Iwo Bialynicki-Birula on his 80th birthday, who inspired much of this work

References in corpus (8)

• Entanglement detection
• Observation of quantum state collapse and revival due to the single-photon Kerr effect
• Imaging high-dimensional spatial entanglement with a camera
• Formulation of the uncertainty relations in terms of the Renyi entropies
• Observation of atom pairs in spontaneous four wave mixing of two colliding Bose-Einstein Condensates
• Violation of Continuous Variable EPR Steering with Discrete Measurements
• Optimal Uncertainty Relations for Extremely Coarse-grained Measurements
• Detection of transverse entanglement in phase space

Cited by in corpus (33)

• Quantifying high dimensional entanglement with two mutually unbiased bases
• Majorization approach to entropic uncertainty relations for coarse-grained observables
• Quantifying high-dimensional entanglement with Einstein-Podolsky-Rosen correlations
• Adaptive phase estimation with two-mode squeezed-vacuum and parity measurement
• Bipartite entanglement of quantum states in a pair basis
• Certification of high-dimensional entanglement and Einstein-Podolsky-Rosen steering with cold atomic quantum memory
• Twin Photon Correlations in Single-Photon Interference
• Entropic uncertainty relations for successive measurements of canonically conjugate observables
• Experimental implementation of the optical fractional Fourier transform in the time-frequency domain
• Mutual Unbiasedness in Coarse-grained Continuous Variables
• Detecting entanglement of continuous variables with three mutually unbiased bases
• Uncertainty Relations for coarse-grained measurements: an overview
• Hierarchies of multipartite entanglement for continuous-variable states
• Gaussian states under coarse-grained continuous variable measurements
• Ancilla-assisted measurement of photonic spatial correlations and entanglement
• Entropic measures of joint uncertainty: effects of lack of majorization
• Missing data outside the detector range: application to continuous variable entanglement verification and quantum cryptography
• Testing for entanglement with periodic coarse-graining
• Uncertainty-Reality Complementarity and Entropic Uncertainty Relations
• Detecting continuous variable entanglement in phase space with the $Q$-distribution
• General class of continuous variable entanglement criteria
• Verifying single-mode nonclassicality beyond negativity in phase space
• Continuous-Variable Nonclassicality Detection under Coarse-Grained Measurement
• Rényi formulation of entanglement criteria for continuous variables
• Mutually Unbiased Coarse-Grained Measurements of Two or More Phase-Space Variables
• Accessing continuous-variable entanglement witnesses with multimode spin observables
• Violations of entropic Bell inequalities with coarse-grained quadrature measurements for continuous-variable states
• Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts
• Interferometric detection of continuous-variable entanglement using two states
• Parametric Competition in non-autonomous Hamiltonian Systems
• Periodic discretized continuous observables are neither continuous nor discrete
• Detecting strongly non-Gaussian entanglement
• Quantum Metrology under Coarse-Grained Measurement