Operational Quantification of Continuous Variable Correlations

Abstract

We quantify correlations (quantum and/or classical) between two continuous variable modes in terms of how many correlated bits can be extracted by measuring the sign of two local quadratures. On Gaussian states, such `bit quadrature correlations' majorize entanglement, reducing to an entanglement monotone for pure states. For non-Gaussian states, such as photonic Bell states, ideal and real de-Gaussified photon-subtracted states, and mixtures of pure Gaussian states, the bit correlations are shown to be a {\em monotonic} function of the negativity. This yields a feasible, operational way to quantitatively measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without a full tomographical reconstruction of the Wigner function.

4 pages, 3 figures, improved presentation, a subfigure and some explicit analytical expressions added

References in corpus (22)

• A computable measure of entanglement
• Quantum information with continuous variables
• Universal Quantum Computation with Continuous-Variable Cluster States
• Entanglement in continuous variable systems: Recent advances and current perspectives
• On the quantum, classical and total amount of correlations in a quantum state
• Generation of a superposition of odd photon number states for quantum information networks
• On the impossibility of distilling Gaussian states with Gaussian operations
• The characterization of Gaussian operations and Distillation of Gaussian States
• Gaussian transformations and distillation of entangled Gaussian states
• Inseparability criteria for bipartite quantum states
• Increasing entanglement between Gaussian states by coherent photon subtraction
• Extremality of Gaussian quantum states
• Proposal for a loophole-free Bell test using homodyne detection
• Controllable generation of highly nonclassical states from nearly pure squeezed vacua
• Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states
• Proposed Test of Quantum Nonlocality for Continuous Variables
• Continuous variable quantum teleportation with non-Gaussian resources
• Optimal States for Bell inequality Violations using Quadrature Phase Homodyne Measurements
• Continuous-variable Werner state: separability, nonlocality, squeezing and teleportation
• Loophole-free test of quantum non-locality using high-efficiency homodyne detectors
• Key distillation from Gaussian states by Gaussian operations
• Efficiency in Quantum Key Distribution Protocols with Entangled Gaussian States

Cited by in corpus (12)

• Spatial correlations in parametric down-conversion
• Entropic Entanglement Criteria for Continuous Variables
• Schur complement inequalities for covariance matrices and monogamy of quantum correlations
• Gaussian geometric discord
• A Family of Continuous Variable Entanglement Criteria using General Entropy Functions
• Nonclassical correlations in continuous-variable non-Gaussian Werner states
• Strong subadditivity for log-determinant of covariance matrices and its applications
• Entropic entanglement criteria in phase space
• Experimentally friendly bounds on non-Gaussian entanglement from second moments
• General class of continuous variable entanglement criteria
• Nonexistence of entangled continuous-variable Werner states with positive partial transpose
• Detecting strongly non-Gaussian entanglement