Schur complement inequalities for covariance matrices and monogamy of quantum correlations

Abstract

We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This allows us to prove general results on the monogamy of entanglement and steering quantifiers in continuous variable systems with an arbitrary number of modes per party. A powerful hierarchical relation for correlation measures based on the log-determinant of covariance matrices is further established for all Gaussian states, which has no counterpart among quantities based on the conventional von Neumann entropy.

arXiv comment5+8 pages. Results improved in Theorem 4. Close to published version

References in corpus (46)

• Quantum entanglement
• A computable measure of entanglement
• Distributed Entanglement
• Classical, quantum and total correlations
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• The logarithmic negativity: A full entanglement monotone that is not convex
• Quantum key distribution using gaussian-modulated coherent states
• Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed states of light
• Granger causality and transfer entropy are equivalent for Gaussian variables
• A gravitational wave observatory operating beyond the quantum shot-noise limit: Squeezed light in application
• Quantum teleportation between light and matter
• Distillation of secret key and entanglement from quantum states
• Continuous variable quantum information: Gaussian states and beyond
• Entanglement in continuous variable systems: Recent advances and current perspectives
• General Monogamy Inequality for Bipartite Qubit Entanglement
• On the quantum, classical and total amount of correlations in a quantum state
• Monogamy of entanglement and other correlations
• 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
• The Real Symplectic Groups in Quantum Mechanics and Optics
• Quantification of Gaussian quantum steering
• Aspects of generic entanglement
• Hudson's Theorem for finite-dimensional quantum systems
• Extremality of Gaussian quantum states
• Is Entanglement Monogamous?
• Observation of genuine one-way Einstein-Podolsky-Rosen steering
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Monogamy of nonlocal quantum correlations
• Deterministic quantum teleportation between distant atomic objects
• Gaussian Entanglement of Formation
• Are general quantum correlations monogamous?
• The resource theory of steering
• Monogamy inequality for distributed Gaussian entanglement
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• Should Entanglement Measures be Monogamous or Faithful?
• Strong Monogamy of Bipartite and Genuine Multipartite Entanglement: The Gaussian Case
• On symplectic eigenvalues of positive definite matrices
• Monogamy equalities for qubit entanglement from Lorentz invariance
• Gaussian quantum marginal problem
• Einstein-Podolsky-Rosen steering measure for two-mode continuous variable states
• Quantum steering of Gaussian states via non-Gaussian measurements
• Strong subadditivity for log-determinant of covariance matrices and its applications
• Stabilizer information inequalities from phase space distributions
• Operational Quantification of Continuous Variable Correlations
• Experimentally friendly bounds on non-Gaussian entanglement from second moments

Cited by in corpus (43)

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• Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications
• Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states
• Gaussian quantum resource theories
• Steering a single system sequentially by multiple observers
• Gaussian entanglement revisited
• Monogamy of entanglement without inequalities
• Continuous variable steering and incompatibility via state-channel duality
• Versatile Multipartite Einstein-Podolsky-Rosen Steering via a Quantum Frequency Comb
• Controlling Stationary One-Way Steering via Thermal Effects in Optomechanics
• Temperature driven quenches in the Ising model: appearance of negative Rényi mutual information
• Demonstrating shareability of multipartite Einstein-Podolsky-Rosen steering
• Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement
• Multipartite Einstein-Podolsky-Rosen steering sharing with separable states
• Full multipartite steering inseparability, genuine multipartite steering and monogamy for continuous variable systems
• Any entanglement of assistance is polygamous
• Rényi Mutual Information in Quantum Field Theory
• Limits on sequential sharing of nonlocal advantage of quantum coherence
• Investigating Einstein-Podolsky-Rosen steering of continuous variable bipartite states by non-Gaussian pseudospin measurements
• From log-determinant inequalities to Gaussian entanglement via recoverability theory
• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Gaussian tripartite steering in Schwarzschild black hole
• Non-classical correlations in quantum mechanics and beyond
• Quantification of Wigner Negativity Remotely Generated via Einstein-Podolsky-Rosen Steering
• Extendibility of bosonic Gaussian states
• Assisted concentration of Gaussian resources
• On the Strong Subadditivity of the Rényi entropies for bosonic and fermionic Gaussian states
• Quantification of quantum steering in a Gaussian Greenberger-Horne-Zeilinger state
• Page curves and typical entanglement in linear optics
• Homodyne detection of non-Gaussian quantum steering
• Shareability of steering in 2-producible states
• Experimental Test of Nonlocality Limits from Relativistic Independence
• Faithful geometric measures for genuine tripartite entanglement
• Exploring Shallow-Depth Boson Sampling: Towards Scalable Quantum Supremacy
• On Quantum Steering and Wigner Negativity
• Quantification of Quantum Correlations in Two-Beam Gaussian States Using Photon-Number Measurements
• Demonstration of monogamy laws for Gaussian steering in optomechanics
• Coupled three-mode squeezed vacuum: Gaussian steering and remote generation of Wigner negativity
• Fundamental limitations to key distillation from Gaussian states with Gaussian operations
• Optimal secure quantum teleportation of coherent states of light
• The polygon relation and subadditivity of entropic measures for discrete and continuous multipartite entanglement
• Exploiting Gaussian steering to probe non-Markovianity due to the interaction with a structured environment
• Tripartite entanglement and tripartite steering in three-qubit pure states induced by vacuum--one-photon superpositions