Exploring multipartite quantum correlations with the square of quantum discord

Abstract

We explore the quantum correlation distribution in multipartite quantum states based on the square of quantum discord (SQD). For tripartite quantum systems, we derive the necessary and sufficient condition for the SQD to satisfy the monogamy relation. Particularly, we prove that the SQD is monogamous for three-qubit pure states, based on which a genuine tripartite quantum correlation measure is introduced. In addition, we also address the quantum correlation distributions in four-qubit pure states. As an example, we investigate multipartite quantum correlations in the dynamical evolution of multipartite cavity-reservoir systems.

arXiv comment8 pages, 5 figures

References in corpus (59)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Introducing Quantum Discord
• Three qubits can be entangled in two inequivalent ways
• Distributed Entanglement
• Classical, quantum and total correlations
• Finite-Time Disentanglement via Spontaneous Emission
• The classical-quantum boundary for correlations: discord and related measures
• Quantum discord and the power of one qubit
• Necessary and sufficient condition for non-zero quantum discord
• On the Power of One Bit of Quantum Information
• Experimental quantum computing without entanglement
• Quantum discord for two-qubit X-states
• Unified View of Quantum and Classical Correlations
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Monogamy of entanglement and other correlations
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Sudden transition between classical and quantum decoherence
• Classical and quantum correlations under decoherence
• Quantum versus classical correlations in Gaussian states
• Gaussian quantum discord
• Quantum discord as resource for remote state preparation
• Experimental investigation of classical and quantum correlations under decoherence
• No-local-broadcasting theorem for quantum correlations
• Sudden Birth Versus Sudden Death of Entanglement in Multipartite Systems
• Dynamics of quantum entanglement
• Interpreting quantum discord through quantum state merging
• Operational interpretations of quantum discord
• Global Quantum Discord in Multipartite Systems
• Quantum discord of two-qubit X-states
• Dynamics of quantum correlations in two-qubit systems within non-Markovian environments
• Quantum Discord and the Geometry of Bell-Diagonal States
• Entangled three-qubit states without concurrence and three-tangle
• Conservation law for distributed entanglement of formation and quantum discord
• Are general quantum correlations monogamous?
• Environment-induced sudden transition in quantum discord dynamics
• Genuine quantum and classical correlations in multipartite systems
• Monogamy properties of quantum and classical correlations
• Conditions for Monogamy of Quantum Discord: Greenberger-Horne-Zeilinger versus W states
• Ordering States with Entanglement Measures
• Entanglement monogamy and entanglement evolution in multipartite systems
• Broadcast copies reveal the quantumness of correlations
• Quantum phases with differing computational power
• Postulates for measures of genuine multipartite correlations
• Quantum discord as a resource in quantum communication
• On the optimal measurement for quantum discord of two-qubit states
• Quantum discord and multipartite correlations
• Quantum Dissension: Generalizing Quantum Discord for Three-Qubit States
• Quantifying quantum discord and entanglement of formation via unified purifications
• Entropic measures of nonclassical correlations
• Multipartite quantum correlation and entanglement in four-qubit pure states
• Necessary and sufficient conditions of freezing phenomena of quantum discord under phase damping
• Multipartite entanglement in four-qubit cluster-class states
• Why the Entanglement of Formation is not generally monogamic
• Hot entanglement in a simple dynamical model
• On two-qubit states ordering with quantum discords
• Entanglement in a class of multiqubit mixed states without multipartite tangles
• Quantum Discord for Investigating Quantum Correlations without Entanglement in Solids
• Entanglement evolution in multipartite cavity-reservoir systems under local unitary operations

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• Quantum discord and its allies: a review
• General monogamy relation for the entanglement of formation in multiqubit systems
• Entanglement monogamy relations of qubit systems
• Monogamy of quantum correlations - a review
• Monogamy of entanglement of formation
• General Monogamy of Tsallis $q$-Entropy Entanglement in Multiqubit Systems
• Tighter monogamy relations in multipartite systems
• Tighter entanglement monogamy relations of qubit systems
• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
• Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems
• All Multiparty Quantum States Can Be Made Monogamous
• Do Large Number of Parties Enforce Monogamy in All Quantum Correlations?
• Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement
• Tighter constraints of multiqubit entanglement
• Enhancement of Quantum Correlation Length in Quenched Disordered Spin Chains
• Local quantum uncertainty for multipartite quantum systems
• Conditions for monogamy of quantum correlations in multipartite systems
• Monogamy of quantum discord
• Universality in Distribution of Monogamy Scores for Random Multiqubit Pure States
• Shared Purity of Multipartite Quantum States
• Generalized monogamy inequalities of convex-roof extended negativity in $N$-qubit systems
• Long-range multipartite quantum correlations and factorization in a one-dimensional spin-1/2 $XY$ chain
• Monogamy relations of all quantum correlation measures for multipartite quantum systems
• Genuine multipartite correlations in Dicke Superradiance
• Generalised monogamy relation of convex-roof extended negativity in multi-level systems
• Diagnosing Quantum Phases Using Long-Range Two-Site Quantum Resource Behaviors
• Tighter monogamy and polygamy relations of quantum entanglement in multi-qubit systems
• Tsallis entropy, $q$-expectation and constraints on three-party quantum correlations
• Trade-off relations of l_1-norm coherence for multipartite systems
• Monogamy relations for nonclassical correlations of multi-qubit states
• General Monogamy and polygamy properties of quantum systems
• What does monogamy in higher powers of a correlation measure mean?
• Entanglement and measurement-induced nonlocality of mixed maximally entangled states in multipartite dynamics
• Correlation evolution and monogamy of two geometric quantum discords in multipartite systems
• Note on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures
• Maximum Violation of Monogamy of Entanglement for Indistinguishable Particles by Measures that are Monogamous for Distinguishable Particles
• Restrictions on shareability of classical correlations for random multipartite quantum states
• Reexamination of strong subadditivity: A quantum-correlation approach
• Generalized product-form monogamy relations in multi-qubit systems
• Genuine tripartite entanglement in Bhabha scattering with an entangled spectator particle
• Scaling of quantum correlation and monogamy relation near a quantum phase transitions in two-dimensional XY spin system
• Monogamy inequalities for entanglement using continuous variable measurements
• Monogamous nature of symmetric multiqubt states with distinct spinors