Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode states

Abstract

Certification and quantification of correlations for multipartite states of quantum systems appear to be a central task in quantum information theory. We give here a unitary quantum-mechanical perspective of both entanglement and Einstein-Podolsky-Rosen (EPR) steering of continuous-variable multimode states. This originates in the Heisenberg uncertainty relations for the canonical quadrature operators of the modes. Correlations of two-party $(N\text{vs}1)$-mode states are examined by using the variances of a pair of suitable EPR-like observables. It turns out that the uncertainty sum of these nonlocal variables is bounded from below by local uncertainties and is strengthened differently for separable states and for each one-way unsteerable ones. The analysis of the minimal properly normalized sums of these variances yields necessary conditions of separability and EPR unsteerability of $(N\text{vs}1)$-mode states in both possible ways of steering. When the states and the performed measurements are Gaussian, then these conditions are precisely the previously-known criteria of separability and one-way unsteerability.

References in corpus (43)

• Quantum entanglement
• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Separability of Mixed States: Necessary and Sufficient Conditions
• Peres-Horodecki separability criterion for continuous variable systems
• Inseparability criterion for continuous variable systems
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Continuous variable quantum information: Gaussian states and beyond
• The Einstein-Podolsky-Rosen paradox: from concepts to applications
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Quantum Steering
• Information-theoretic aspects of quantum inseparability of mixed states
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Detecting genuine multipartite continuous-variable entanglement
• Bound entangled Gaussian states
• Violation of local uncertainty relations as a signature of entanglement
• Quantification of Gaussian quantum steering
• Observation of one-way Einstein-Podolsky-Rosen steering
• Quantifying Einstein-Podolsky-Rosen steering
• Extremality of Gaussian quantum states
• Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
• Joint measurability of generalized measurements implies classicality
• Building Gaussian Cluster States by Linear Optics
• Characterizing the entanglement of bipartite quantum systems
• Negativity and steering: a stronger Peres conjecture
• Covariance matrices and the separability problem
• Classifying directional Gaussian quantum entanglement, EPR steering and discord
• Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems
• Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion
• Gaussian entanglement revisited
• Continuous variable steering and incompatibility via state-channel duality
• Bures distance as a measure of entanglement for symmetric two-mode Gaussian states
• Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture
• Einstein-Podolsky-Rosen steering measure for two-mode continuous variable states
• Quantum Fisher information on two manifolds of two-mode Gaussian states
• Detecting Einstein-Podolsky-Rosen steering through entanglement detection
• Steering Criteria via Covariance Matrices of Local Observables in Arbitrary Dimensional Quantum Systems
• Breaking Gaussian incompatibility on continuous variable quantum systems
• Standard forms and entanglement engineering of multimode Gaussian states under local operations
• Gaussian local unitary equivalence of $n$-mode Gaussian states and Gaussian transformations by local operations with classical communication
• Einstein-Podolsky-Rosen-like separability indicators for two-mode Gaussian states

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