Are general quantum correlations monogamous?

Abstract

Quantum entanglement and quantum non-locality are known to exhibit monogamy, that is, they obey strong constraints on how they can be distributed among multipartite systems. Quantum correlations that comprise and go beyond entanglement are quantified by, e.g., quantum discord. It was observed recently that for some states quantum discord is not monogamous. We prove in general that any measure of correlations that is monogamous for all states and satisfies reasonable basic properties must vanish for all separable states: only entanglement measures can be strictly monogamous. Monogamy of other than entanglement measures can still be satisfied for special, restricted cases: we prove that the geometric measure of discord satisfies the monogamy inequality on all pure states of three qubits.

5 pages, 1 figure, added a discussion of our main result in relation to the fact that separable states are infinitely shareable

References in corpus (29)

• Quantum discord and the power of one qubit
• Necessary and sufficient condition for non-zero quantum discord
• Experimental quantum computing without entanglement
• General Monogamy Inequality for Bipartite Qubit Entanglement
• No-local-broadcasting theorem for quantum correlations
• A complete family of separability criteria
• Interpreting quantum discord through quantum state merging
• Operational interpretations of quantum discord
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Linking Quantum Discord to Entanglement in a Measurement
• All non-classical correlations can be activated into distillable entanglement
• Is Entanglement Monogamous?
• Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
• Conservation law for distributed entanglement of formation and quantum discord
• Monogamy inequality for distributed Gaussian entanglement
• Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality
• Monogamy properties of quantum and classical correlations
• Genuine quantum and classical correlations in multipartite systems
• Entanglement irreversibility from quantum discord and quantum deficit
• Conditions for Monogamy of Quantum Discord: Greenberger-Horne-Zeilinger versus W states
• Experimentally Witnessing the Quantumness of Correlations
• Interplay between computable measures of entanglement and other quantum correlations
• Entanglement, discord and the power of quantum computation
• Monogamy of Bell's inequality violations in non-signaling theories
• Broadcast copies reveal the quantumness of correlations
• A simple proof of monogamy of entanglement
• The quantumness of correlations revealed in local measurements exceeds entanglement
• Quantum discord and classical correlations in the bond-charge Hubbard model: quantum phase transitions, ODLRO and violation of the monogamy property for discord
• Discord and non-classicality in probabilistic theories

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• Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence
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• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• Universal freezing of quantum correlations within the geometric approach
• Should Entanglement Measures be Monogamous or Faithful?
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• Distributed correlations and information flows within a hybrid multipartite quantum-classical system
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• Monogamy of Quantum Discord by Multipartite Correlations
• Quantum discord in the ground state of spin chains
• All Multiparty Quantum States Can Be Made Monogamous
• Anisotropic invariance and the distribution of quantum correlations
• Generalized Geometric Measure of Entanglement for Multiparty Mixed States
• Entanglement Polygon Inequality in Qubit Systems
• Monogamy of correlations and entropy inequalities in the Bloch picture
• Multipartite monogamy of the concurrence
• Monogamy, polygamy, and other properties of entanglement of purification
• Nonviolation of Bell's Inequality in Translation Invariant Systems
• Quantumness of correlations, quantumness of ensembles and quantum data hiding
• Do Large Number of Parties Enforce Monogamy in All Quantum Correlations?
• Strong monogamy inequalities for four qubits
• Compatible quantum correlations: on extension problems for Werner and isotropic states
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• The dynamic behaviors of local quantum uncertainty for three-qubit X states under decoherence channels
• Extracting Information from Qubit-Environment Correlations
• Full multipartite steering inseparability, genuine multipartite steering and monogamy for continuous variable systems
• Any entanglement of assistance is polygamous
• Limits on sequential sharing of nonlocal advantage of quantum coherence
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• Conditions for monogamy of quantum correlations in multipartite systems
• Computable genuine multimode entanglement measure: Gaussian vs. non-Gaussian
• Monogamy and backflow of mutual information in non-Markovian thermal baths
• Monogamy deficit for quantum correlation in multipartite quantum system
• The One-Way Information Deficit and Geometry for a Class of Two-qubit States
• Multipartite quantum correlations in even and odd spin coherent states
• Decoherence Dynamics of Measurement-Induced Nonlocality and comparison with Geometric Discord for two qubit systems
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• Violation of Bell inequality in perfect translation invariant systems
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• Universality in Distribution of Monogamy Scores for Random Multiqubit Pure States
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• Lower bounds on violation of monogamy inequality for quantum correlation measures
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• Shared Purity of Multipartite Quantum States
• Generalized monogamy inequalities of convex-roof extended negativity in $N$-qubit systems
• Tighter monogamy relations of multiqubit entanglement in terms of Rényi-$\alpha$ entanglement
• Role of weak measurements on states ordering and monogamy of quantum correlation
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• Monogamy inequality in terms of entanglement measures based on distance for pure multiqubit states
• Information complementarity in multipartite quantum states and security in cryptography
• Monogamy of Entanglement Measures Based on Fidelity in Multiqubit Systems
• Delocalization of quantum information in long-range interacting systems
• Global quantum correlations in tripartite nonorthogonal states and monogamy properties
• Distribution of Bell inequality violation vs. multiparty quantum correlation measures
• Monogamy of Logarithmic Negativity and Logarithmic Convex-Roof Extended Negativity
• Complete Genuine Multipartite Entanglement Monotone
• Quantum correlations from classically correlated states
• Tsallis entropy, $q$-expectation and constraints on three-party quantum correlations
• Entanglement distribution and quantum discord
• Activation of Nonmonogamous Multipartite Quantum States
• Trade-off relations of l_1-norm coherence for multipartite systems
• Monogamy relations for nonclassical correlations of multi-qubit states
• Partial-Norm of Entanglement: Entanglement Monotones That are not Monogamous
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• Thermal quantum discord in the Heisenberg chain with impurity
• Distribution of Mutual Information in Multipartite States
• Additivity relations in quantum correlations
• Correlation evolution and monogamy of two geometric quantum discords in multipartite systems
• What does monogamy in higher powers of a correlation measure mean?
• Note on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures
• Genuine correlations in finite-size spin systems
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• Restrictions on shareability of classical correlations for random multipartite quantum states
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