Monogamy of entanglement and other correlations

Abstract

It has been observed by numerous authors that a quantum system being entangled with another one limits its possible entanglement with a third system: this has been dubbed the "monogamous nature of entanglement". In this paper we present a simple identity which captures the trade-off between entanglement and classical correlation, which can be used to derive rigorous monogamy relations. We also prove various other trade-offs of a monogamy nature for other entanglement measures and secret and total correlation measures.

7 pages, revtex4

References in corpus (1)

• Entanglement Cost of Three-Level Antisymmetric States

Cited by in corpus (365)

• Quantum entanglement
• The classical-quantum boundary for correlations: discord and related measures
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Quantum versus classical correlations in Gaussian states
• Jerusalem Lectures on Black Holes and Quantum Information
• Fundamental rate-loss tradeoff for optical quantum key distribution
• Leggett-Garg Inequalities
• Security in Quantum Cryptography
• Measures and applications of quantum correlations
• Aspects of generic entanglement
• Interpreting quantum discord through quantum state merging
• Operational interpretations of quantum discord
• Holographic Mutual Information is Monogamous
• Conjectured Strong Complementary Information Tradeoff
• Computing quantum discord is NP-complete
• Simulation methods for open quantum many-body systems
• Quantum discord and its allies: a review
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Distribution of quantum coherence in multipartite systems
• Faithful Squashed Entanglement
• Behavior of Quantum Correlations under Local Noise
• Non-Markovianity through accessible information
• Quantum discord as a resource for quantum cryptography
• Conservation law for distributed entanglement of formation and quantum discord
• Are general quantum correlations monogamous?
• General monogamy relation for the entanglement of formation in multiqubit systems
• Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory
• Irreversibility for all bound entangled states
• Entanglement monogamy relations of qubit systems
• Generic emergence of classical features in quantum Darwinism
• Tightening the entropic uncertainty bound in the presence of quantum memory
• Monogamy of quantum correlations - a review
• Duality for monogamy of entanglement
• Competitions between quantum correlations in the quantum-memory-assisted entropic uncertainty relation
• The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography
• Monogamy properties of quantum and classical correlations
• Genuine quantum and classical correlations in multipartite systems
• Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions
• Geometric quantum discord with Bures distance
• Relative quantum coherence, incompatibility, and quantum correlations of states
• Entanglement irreversibility from quantum discord and quantum deficit
• Conditions for Monogamy of Quantum Discord: Greenberger-Horne-Zeilinger versus W states
• Upper bound and shareability of quantum discord based on entropic uncertainty relations
• The squashed entanglement of a quantum channel
• Correlations in Grover search
• Monogamy and polygamy for multi-qubit entanglement using Rényi entropy
• Non-Markovianity through flow of information between a system and an environment
• Unitarity of black hole evaporation in final-state projection models
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• Monogamy of entanglement of formation
• Quantum-memory-assisted entropic uncertainty relations
• Entanglement of Purification for Multipartite States and its Holographic Dual
• Quantum Dynamics as an analog of Conditional Probability
• Should Entanglement Measures be Monogamous or Faithful?
• Monogamy of Correlations vs. Monogamy of Entanglement
• Optimality of Gaussian Discord
• Exploring multipartite quantum correlations with the square of quantum discord
• Schur complement inequalities for covariance matrices and monogamy of quantum correlations
• Quantum correlations between each qubit in a two-atom system and the environment in terms of interatomic distance
• A temporal steering inequality
• Monogamy of Bell's inequality violations in non-signaling theories
• Inequalities for the Ranks of Quantum States
• Tighter monogamy relations in multipartite systems
• Quantum discord as a resource in quantum communication
• Distillation of local purity from quantum states
• Unified entropy, entanglement measures and monogamy of multi-party entanglement
• Assisted state discrimination without entanglement
• Quantum correlations and distinguishability of quantum states
• Entanglement Monogamy of Tripartite Quantum States
• Analytical characterization of the genuine multiparticle negativity
• Quantum-correlating power of local quantum channels
• Quantum Discord and its Role in Quantum Information Theory
• Monogamy of entanglement without inequalities
• Entanglement Sharing and Decoherence in the Spin-Bath
• Cost of quantum entanglement simplified
• Quantum discord cannot be shared
• Negativity and strong monogamy of multi-party quantum entanglement beyond qubits
• Quantum discord of two-qubit rank-two states
• Polygamy of Distributed Entanglement
• Tighter entanglement monogamy relations of qubit systems
• Orthogonal measurements are {\it almost} sufficient for quantum discord of two qubits
• On Hastings' counterexamples to the minimum output entropy additivity conjecture
• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
• Fidelity of recovery, geometric squashed entanglement, and measurement recoverability
• Quantum entanglement in the triangle network
• A simple proof of monogamy of entanglement
• Topological phases of a dimerized Fermi-Hubbard model for semiconductor nano-lattices
• Semidefinite programming relaxations for quantum correlations
• Squashed entanglement, k-extendibility, quantum Markov chains, and recovery maps
• Attacking the Quantum Internet
• Concurrence vs. purity: Influence of local channels on Bell states of two qubits
• Limitations to sharing entanglement
• Quantifying quantum discord and entanglement of formation via unified purifications
• The correlation theory of the chemical bond
• Monogamy equalities for qubit entanglement from Lorentz invariance
• On quantum advantage in dense coding
• Measurement-induced disturbances and nonclassical correlations of Gaussian states
• The Feynman problem and Fermionic entanglement: Fermionic theory versus qubit theory
• Relative entropy and squashed entanglement
• Multipartite Entanglement Measure and Complete Monogamy Relation
• Entanglement of Purification in Free Scalar Field Theories
• Entanglement cost and quantum channel simulation
• Eavesdropping on the Decohering Environment: Quantum Darwinism, Amplification, and the Origin of Objective Classical Reality
• Geometric picture of quantum discord for two-qubit quantum states
• Locally Inaccessible Information as a Fundamental Ingredient to Quantum Information
• Monogamy of the Entanglement of Formation
• Holographic spacetime, black holes and quantum error correcting codes: A review
• Quantum and Classical Correlations Inside the Entanglement Wedge
• Entanglement entropy, entropy production and time evolution in high energy QCD
• Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems
• Monogamy of quantum correlations in three qubit pure states using Rajagopal-Rendell (RR) quantum deficit
• General polygamy inequality of multi-party quantum entanglement
• Monogamy of quantum correlations reveals frustration in a quantum Ising spin system: Experimental demonstration
• Generalized Geometric Measure of Entanglement for Multiparty Mixed States
• All Multiparty Quantum States Can Be Made Monogamous
• Strong superadditivity and monogamy of the Renyi measure of entanglement
• Why the Entanglement of Formation is not generally monogamic
• From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking
• Tightening the tripartite quantum memory assisted entropic uncertainty relation
• Frustration, Entanglement, and Correlations in Quantum Many Body Systems
• Amortized entanglement of a quantum channel and approximately teleportation-simulable channels
• Genuine multipartite entanglement of symmmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing structure
• Monogamy of correlations and entropy inequalities in the Bloch picture
• Are all maximally entangled states pure?
• Complementarity Relations Between Quantum Steering Criteria
• Nonclassical correlations in continuous-variable non-Gaussian Werner states
• Multipartite monogamy of the concurrence
• Weaker entanglement guarantees stronger entanglement
• Rényi squashed entanglement, discord, and relative entropy differences
• Characterization of Tripartite Quantum States with Vanishing Monogamy Score
• Entanglement Islands in Generalized Two-dimensional Dilaton Black Holes
• Thermal quantum and classical correlations in two qubit XX model in a nonuniform external magnetic field
• Phase-Matching Quantum Cryptographic Conferencing
• Trade-off Relations of Bell Violations among Pairwise Qubit Systems
• Strong monogamy inequalities for four qubits
• Do Large Number of Parties Enforce Monogamy in All Quantum Correlations?
• Requirement of Dissonance in Assisted Optimal State Discrimination
• Light Cone-Like Behavior of Quantum Monogamy Score and Multisite Entanglement
• k-stretchability of entanglement, and the duality of k-separability and k-producibility
• A quasipolynomial-time algorithm for the quantum separability problem
• Necessary and sufficient condition for saturating the upper bound of quantum discord
• Useful multipartite correlations from useless reduced states
• Non-Gaussian quantum discord for Gaussian states
• Squashed entanglement and approximate private states
• Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement
• Rényi generalizations of quantum information measures
• Continuous variable methods in relativistic quantum information: Characterisation of quantum and classical correlations of scalar field modes in noninertial frames
• Analytical solution and entanglement swapping of a double Jaynes-Cummings model in non-Markovian environments
• Sequential State Discrimination and Requirement of Quantum Dissonance
• Monogamy inequality for any local quantum resource and entanglement
• Quantum Discord for $d\otimes 2$ Systems
• Exclusion Principle for Quantum Dense Coding
• Correlation measures and distillable entanglement in AdS/CFT
• Extracting Information from Qubit-Environment Correlations
• Distribution of entanglement and correlations in all finite dimensions
• Simultaneous classical-quantum capacities of quantum multiple access channels
• Maximally dense coding capable quantum states
• Full multipartite steering inseparability, genuine multipartite steering and monogamy for continuous variable systems
• Energy-constrained two-way assisted private and quantum capacities of quantum channels
• $\alpha$-Logarithmic negativity
• Conditional Mutual Information and Quantum Steering
• Spectrum conditions for symmetric extendible states
• Quantum information
• Extended nonlocal games and monogamy-of-entanglement games
• Quantum Darwinism in a composite system: Objectivity versus classicality
• Observable estimation of entanglement of formation and quantum discord for bipartite mixed quantum states
• Assisted work distillation
• Redundantly amplified information suppresses quantum correlations in many-body systems
• Bounds on entanglement distillation and secret key agreement for quantum broadcast channels
• A Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model
• Exponentially many entanglement and correlation constraints for multipartite quantum states
• Squashed entanglement in infinite dimensions
• Calculation of quantum discord in arbitrary dimensions, especially for X- and other specialized states
• Measurements, quantum discord and parity in spin 1 systems
• General Monogamy Relations of Quantum Entanglement for Multiqubit W-class States
• Quantum Shannon Theory
• Black holes as clouded mirrors: the Hayden-Preskill protocol with symmetry
• Entanglement Theory and the Quantum Simulation of Many-Body Physics
• Finer Distribution of Quantum Correlations among Multiqubit Systems
• Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous variable systems
• From log-determinant inequalities to Gaussian entanglement via recoverability theory
• Exponential shortcut to measurement-induced entanglement phase transitions
• Quantum Broadcast Channels with Cooperating Decoders: An Information-Theoretic Perspective on Quantum Repeaters
• Multipartite Quantum Correlations in Open Quantum Systems
• Firewalls and flat mirrors: An alternative to the AMPS experiment which evades the Harlow-Hayden obstacle
• Quantumness of Gaussian Discord: Experimental Evidence and Role of System-Environment Correlations
• Asymptotic Entanglement Dynamics and Geometry of Quantum States
• Complementarity between Tripartite Quantum Correlation and Bipartite Bell Inequality Violation in Three Qubit States
• Complete complementarity relations: Connections with EPR realism and decoherence and extension to mixed quantum states
• Entanglement entropy for non-coplanar regions in quantum field theory
• On Strong Monogamy Conjecture in Four-Qubit System
• Authentication protocol based on collective quantum steering
• Entanglement of formation for a class of $(2\otimes d)$-dimensional systems
• Monogamy and backflow of mutual information in non-Markovian thermal baths
• A Field Theory Study of Entanglement Wedge Cross Section: Odd Entropy
• Complementary Quantum Correlations among Multipartite Systems
• Monogamy deficit for quantum correlation in multipartite quantum system
• Tighter monogamy relations of quantum entanglement for multiqubit W-class states
• Sequential state discrimination with quantum correlation
• Multipartite quantum correlations in even and odd spin coherent states
• Unification of multi-qubit polygamy inequalities
• Conclusive Identification of Quantum Channels via Monogamy of Quantum Correlations
• Sudden Change of Quantum Discord under Single Qubit Noise
• Quantum discord of Bell cat-states under amplitude damping
• Strong monogamy of multi-party quantum entanglement for partially coherently superposed states
• Emergent classicality in general multipartite states and channels
• Entanglement measures and approximate quantum error correction
• Monogamy inequality for entanglement and local contextuality
• The one-way unlocalizable quantum discord
• Entanglement fidelity of quantum memories
• A convergent inflation hierarchy for quantum causal structures
• Reducing Computational Complexity of Quantum Correlations
• One-body information loss in fermion systems
• Monogamy of quantum entanglement
• Parametric down conversion with a depleted pump as a model for classical information transmission capacity of quantum black holes
• Analytical Expression of Quantum Discord for Rank-2 Two-qubit States
• Classical extension of quantum-correlated separable states
• Robust quantum correlations in out-of-equilibrium matter-light systems
• Generalized conditional entropy optimization for qudit-qubit states
• Continuity of characteristics of composite quantum systems
• Improved monogamy relations with concurrence of assistance and negativity of assistance for multiqubit W-class states
• Forbidden regimes in the distribution of bipartite quantum correlations due to multiparty entanglement
• Global-to-local incompatibility, monogamy of entanglement, and ground-state dimerization: Theory and observability of quantum frustration in systems with competing interactions
• Monogamy of entanglement for tripartite systems
• Concentrating tripartite quantum information
• Generalized conditional entropy in bipartite quantum systems
• When is a Genuine Multipartite Entanglement Measure Monogamous?
• Overcoming Noise Limitations in QKD with Quantum Privacy Amplification
• Resource conversion between operational coherence and multipartite entanglement in many-body systems
• The balance of quantum correlations for a class of feasible tripartite continuous variable states
• Complementarity of genuine multipartite non-locality
• Strict entanglement monotonicity under local operations and classical communication
• Private quantum decoupling and secure disposal of information
• Monogamy relations and upper bounds for the generalized $W$-class states using Rényi-$\alpha$ entropy
• Interference Visibility as a Witness of Entanglement and Quantum Correlation
• Quantum discord and information deficit in spin chains
• Complete monogamy of the multipartite quantum mutual information
• Lower bounds on violation of monogamy inequality for quantum correlation measures
• Monogamy properties of qubit systems
• Universality in Distribution of Monogamy Scores for Random Multiqubit Pure States
• Propagation and Distribution of Quantum Correlations in a Cavity QED Network
• Exact entanglement cost of quantum states and channels under PPT-preserving operations
• Construction of genuinely multipartite entangled subspaces and the associated bounds on entanglement measures for mixed states
• Monogamy and entanglement in tripartite quantum states
• Locally Accessible Information of Multisite Quantum Ensembles Violates Monogamy
• Shared Purity of Multipartite Quantum States
• Exclusion principle for nonlocal advantage of quantum coherence
• Security of entanglement-based QKD with realistic parametric down-conversion sources
• On monogamy and polygamy relations of multipartite systems
• Generalised monogamy relation of convex-roof extended negativity in multi-level systems
• Shielding quantum discord through continuous dynamical decoupling
• Do black holes create polyamory?
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• Entanglement of formation and monogamy of multi-party quantum entanglement
• Continuous-variable dense coding via a general Gaussian state: Monogamy relation
• Monogamy of Information Causality
• Monogamy relations of all quantum correlation measures for multipartite quantum systems
• Information complementarity in multipartite quantum states and security in cryptography
• Realization of the tradeoff between internal and external entanglement
• Global quantum correlations in tripartite nonorthogonal states and monogamy properties
• Tomographic characterisation of correlations in a photonic tripartite state
• Generation and entanglement study of generalized N-mode single photon perfect W-states
• Distribution of Bell inequality violation vs. multiparty quantum correlation measures
• Optimized Correlation Measures in Holography
• Monogamy relation in multipartite continuous-variable quantum teleportation
• Quantum correlations in nanostructured two-impurity Kondo systems
• Amplification, inference, and the manifestation of objective classical information
• Monogamy of Logarithmic Negativity and Logarithmic Convex-Roof Extended Negativity
• Multi-linear Monogamy Relations for Three Qubit States
• Monogamy of Entanglement Measures Based on Fidelity in Multiqubit Systems
• Non-distillable entanglement guarantees distillable entanglement
• Entanglement distribution and quantum discord
• Generalizations of Quantum Discord
• Complete Genuine Multipartite Entanglement Monotone
• Upper Bounds on the Distillable Randomness of Bipartite Quantum States
• Multipartite monogamous relations for Entanglement and Discord
• Entanglement Sharing Protocol via Quantum Error Correcting Codes
• Monogamy and trade-off relations for correlated quantum coherence
• Tsallis entropy, $q$-expectation and constraints on three-party quantum correlations
• Quantifying the unextendibility of entanglement
• Determination of the maximum Global Quantum Discord via measurements of excitations in a cavity QED network
• Quantifying nonlocality as a resource for device-independent quantum key distribution
• Quantum Correlations in Cavity QED Networks
• Activation of Nonmonogamous Multipartite Quantum States
• Characterizing entanglement using quantum discord over state extensions
• Open-destination measurement-device-independent quantum key distribution network
• Correlation measures of a quantum state and information characteristics of a quantum channel
• Partial-Norm of Entanglement: Entanglement Monotones That are not Monogamous
• Tighter generalized monogamy and polygamy relations for multiqubit systems
• Polygamy relations of multipartite entanglement beyond qubits
• What does monogamy in higher powers of a correlation measure mean?
• Pairwise Concurrence in Cyclically Symmetric Quantum States
• On discontinuity of information characteristics of quantum systems and channels
• Quantumness of gravitational field: A perspective on monogamy relation
• Heralded Channel Holevo Superadditivity Bounds from Entanglement Monogamy
• Multipartite quantum and classical correlations in symmetric n-qubit mixed states
• Operator system structures on the unital direct sum of C*-algebras
• Observation of the tradeoff between internal quantum nonseparability and external classical correlations
• Polygamy of multi-party $q$-expected quantum entanglement
• Dissipative dynamics of atom-field entanglement in the ultrastrong-coupling regime
• Strong polygamy of quantum correlations in multi-party quantum systems
• Quantum discord in photon added Glauber coherent states of $\mathrm{GHZ}$-type
• Reduced quantum dynamics with initial system-environment correlations characterized by pure Markov states
• Several Trade off Features of Quantum Steering in Distributed Scenario
• Restrictions on shareability of classical correlations for random multipartite quantum states
• Correlation measures in bipartite states and entanglement irreversibility
• Nonclassical correlations in subsystems of globally entangled quantum states
• Classical and quantum parts of conditional mutual information for open quantum systems
• Squashed Entanglement from Generalized Rindler Wedge
• Monogamy of Nonlocal Games
• Polygamy relation of quantum correlations with equality
• Gaussian intrinsic entanglement for states with partial minimum uncertainty
• Statistics of leading digits leads to unification of quantum correlations
• Quantum discord from system-environment correlations
• Time evolution of the inside of the black hole's horizon
• Quantum Euler relation for local measurements
• Revisiting Deniability in Quantum Key Exchange via Covert Communication and Entanglement Distillation
• Does connected wedge imply distillable entanglement?
• A Quantum Information Perspective on Many-Body Dispersive Forces
• Polygamy Inequalities for Qubit Systems
• Partitions of Correlated N-Qubit Systems
• The Effect of Stationary Axisymmetric Spacetimes in Interferometric Visibility
• Quantifying High-Order Interdependencies in Entangled Quantum States
• Bipartite and tripartite entanglement in a Bose-Einstein acoustic black hole
• Revealing Tripartite Quantum Discord with Tripartite Information Diagram
• Reexamination of strong subadditivity: A quantum-correlation approach
• Extended Nonlocal Games
• Correlation Redistribution by Causal Horizons
• Tighter superadditivity relations for $l_1$-norm coherence measure
• Emergence of Monogamy under Static and Dynamic Scenarios
• Coordinately Assisted Distillation of Quantum Coherence in Multipartite System
• Monogamy of highly symmetric states
• Quantitative bounds to propagation of quantum correlations in many-body systems
• Dynamics of quantum discord in the purification process
• Entanglement Swapping Model of DNA Replication
• Entanglement manipulation by a local magnetic pulse
• Multipartite distribution property of one way discord beyond measurement
• Distribution of Gaussian Entanglement in Linear Optical Systems
• Multipartite Monogamy of Entanglement for Three Qubit States
• Mathematical framework for detection and quantification of nonclassical correlation
• Quantum circuit simulation of black hole evaporation and Maxwell demon interpretation
• Conditional purity and quantum correlation measures in two qubit mixed states
• Strong Subadditivity Lower Bound and Quantum Channels
• Conditional states and entropy in qudit-qubit systems
• Monogamy and polygamy for multi-qudit generalized $W$-class states based on concurrence of assistance and Tsallis-$q$ entanglement of assistance
• A Quantum Algorithm for Finding Common Matches Between Databases with Reliable Behavior
• Monogamous nature of symmetric multiqubt states with distinct spinors
• From Information Theory Puzzles in Deletion Channels to Deniability in Quantum Cryptography
• Is monogamy of entanglement geometrical?
• Correlations in geometric states
• Optimal bound on long-range distillable entanglement
• Probe of Generic Quantum Contextuality and Nonlocal Resources for Qubits
• Monogamy of entanglement of maximal dimension
• Antilinear superoperator, quantum geometric invariance, and antilinear symmetry for higher-dimensional quantum systems
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors
• Testing quantum satisfiability
• Entanglement as the cross-symmetric part of quantum discord
• Realizing fully reference-frame-independent quantum key distribution by exploiting quantum discord
• Genuine tripartite entanglement in Bhabha scattering with an entangled spectator particle
• Monogamy inequalities of entanglement of assistance in $2\otimes 2\otimes d$ systems
• Quantum Monogamy with Predetermined Events
• Computable constraints on entanglement-sharing of multipartite quantum states
• Shareability of Quantum Correlations in a Many-Body Spin System with Two- and Three-Body Interactions
• Some aspects of the interplay between bipartite correlations and quantum channels
• Computable Measure of Total Quantum Correlation of Multipartite Systems