Uncertainty inequalities as entanglement criteria for negative partial-transpose states

Abstract

In this Letter, we show that the fulfillment of uncertainty relations is a sufficient criterion for a quantum-mechanically permissible state. We specifically construct two pseudo-spin observables for an arbitrary non-positive Hermitian matrix whose uncertainty relation is violated. This method enables us to systematically derive separability conditions for all negative partial-transpose states in experimentally accessible forms. In particular, generalized entanglement criteria are derived from the Schrodinger-Robertson inequalities for bipartite continuous-variable states.

4 pages, published version with minor changes

References in corpus (21)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Inseparability criterion for continuous variable systems
• Entangling macroscopic oscillators exploiting radiation pressure
• Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement
• Entanglement conditions for two-mode states
• Inseparability criteria for bipartite quantum states
• A computable measure of nonclassicality for light
• Characterizing the entanglement of bipartite quantum systems
• A theorem for the beam splitter entangler
• Inseparability inequalities for higher-order moments for bipartite systems
• Detecting multimode entanglement by symplectic uncertainty relations
• Multimode uncertainty relations and separability of continuous variable states
• Entanglement conditions for two-mode states: Applications
• Nonlinear entanglement witnesses
• Universal measurement of quantum correlations of radiation
• Entanglement criteria via the uncertainty relations in su(2) and su(1,1) algebra: detection of non-Gaussian entangled states
• Entanglement condition via su(2) and su(1,1) algebra using Schr{ö}dinger-Robertson uncertainty relation
• Does The Uncertainty Relation Determine The Quantum State?
• Unitary equivalence between ordinary intelligent states and generalized intelligent states
• Complete conditions for legitimate Wigner distributions

Cited by in corpus (43)

• Spatial correlations in parametric down-conversion
• Continuous-variable quantum teleportation with non-Gaussian entangled states generated via multiple-photon subtraction and addition
• Information Invariance and Quantum Probabilities
• Entanglement of Gaussian states using beam splitter
• Demonstrating higher-order nonclassical effects by photon-added classical states: Realistic schemes
• A Family of Continuous Variable Entanglement Criteria using General Entropy Functions
• Optimal Uncertainty Relations for Extremely Coarse-grained Measurements
• Revealing nonclassicality beyond Gaussian states via a single marginal distribution
• Entanglement detection via tighter local uncertainty relations
• Efficient entanglement criteria beyond Gaussian limits using Gaussian measurements
• Variance uncertainty relations without covariances for three and four observables
• Detecting and estimating continuous-variable entanglement by local orthogonal observables
• Dynamics-Based Entanglement Witnesses for Non-Gaussian States of Harmonic Oscillators
• Linear amplification and quantum cloning for non-Gaussian continuous variables
• Entanglement criteria and nonlocality for multi-mode continuous variable systems
• Uncertainty Relations for coarse-grained measurements: an overview
• Demonstrating nonclassicality and non-Gaussianity of single-mode fields: Bell-type tests using generalized phase-space distributions
• Hierarchy of Nonlinear Entanglement Dynamics for Continuous Variables
• Many-particle entanglement criterion for superradiant-like states
• Hierarchies of multipartite entanglement for continuous-variable states
• Heisenberg Uncertainty Relation for Coarse-grained Observables
• Detecting non-Markovianity via uncertainty relations
• Non-Gaussianity and entropy-bounded uncertainty relations: Application to detection of non-Gaussian entangled states
• Detecting continuous variable entanglement in phase space with the $Q$-distribution
• Verifying single-mode nonclassicality beyond negativity in phase space
• Generalized Entanglement Measure for Continuous Variable Systems
• Realignment Entanglement Criterion for Continuous Bipartite Symmetric Quantum States
• Detection of bound entanglement in continuous variable systems
• Entanglement without Dissipation: A Touchstone for an exact Comparison of Entanglement Measures
• Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
• Gaussian entanglement witness and refined Werner-Wolf criterion for continuous variables
• Minimum Uncertainty and Entanglement
• Entanglement Detection and Distillation for Arbitrary Bipartite Systems
• Nonclassicality and entanglement for wavepackets
• Anatomy of entanglement and nonclassicality criteria
• Uncertainty relation and inseparability criterion
• Entanglement between uncoupled modes with time-dependent complex frequencies
• Entanglement criteria for two strongly interacting ensembles
• Operator transpose within normal ordering and its applications for quantifying entanglement
• Characterizing the Generalized Einstein-Podolsky-Rosen State and Extensions
• Efficient detection for quantum states containing fewer than $k$ unentangled particles in multipartite quantum systems
• Effect of phase fluctuation and dephasing on the dynamics of entanglement generation in a correlated emission laser
• Characterization of four-qubit states via Bell inequalities