Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems

Abstract

We show exactly that the squared entanglement of formation (SEF) obeys a set of hierarchical monogamy relations for an arbitrary $N$-qubit mixed state. Based on this set of monogamy relations, we are able to construct the set of hierarchical multipartite entanglement indicators for $N$-qubit states, which still work well even when the concurrence-based indicators lose efficacy. As a by-product, an intriguing analytical relation between the entanglement of formation (EOF) and squared concurrence (SC) for an arbitrary mixed state of $2\otimes d$ systems is derived, making the concurrence calculable via the corresponding EOF. Furthermore, we analyze the multipartite entanglement dynamics in composite cavity-reservoir systems with the present set of hierarchical indicators. Moreover, for multilevel systems, it is illustrated that the SEF can be monogamous even if the SC is polygamous.

arXiv comment12 pages, 6 figures

References in corpus (56)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Introducing Quantum Discord
• Three qubits can be entangled in two inequivalent ways
• Concentrating Partial Entanglement by Local Operations
• Entanglement of a Pair of Quantum Bits
• Distributed Entanglement
• Classical, quantum and total correlations
• Persistent entanglement in arrays of interacting particles
• The classical-quantum boundary for correlations: discord and related measures
• Universal state inversion and concurrence in arbitrary dimensions
• Quantum discord for two-qubit X-states
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Monogamy of entanglement and other correlations
• Quantum versus classical correlations in Gaussian states
• Gaussian quantum discord
• "Squashed Entanglement" - An Additive Entanglement Measure
• Sudden Birth Versus Sudden Death of Entanglement in Multipartite Systems
• Concurrence of arbitrary dimensional bipartite quantum states
• Quantum discord of two-qubit X-states
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Dynamics of quantum correlations in two-qubit systems within non-Markovian environments
• Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
• Quantum Discord and the Geometry of Bell-Diagonal States
• Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
• Quantifying entanglement resources
• Entangled three-qubit states without concurrence and three-tangle
• Quantum discord and geometry for a class of two-qubit states
• General monogamy relation for the entanglement of formation in multiqubit systems
• Monogamy inequality for distributed Gaussian entanglement
• Entanglement monogamy relations of qubit systems
• Quantum discord for two-qubit X states: Analytical formula with very small worst-case error
• Violation of monogamy inequality for higher-dimensional objects
• Monogamy and polygamy for multi-qubit entanglement using Rényi entropy
• Monogamy of entanglement of formation
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• Entanglement monogamy and entanglement evolution in multipartite systems
• Concurrence and a proper monogamy inequality for arbitrary quantum states
• Exploring multipartite quantum correlations with the square of quantum discord
• Quantum discord as a resource in quantum communication
• On the optimal measurement for quantum discord of two-qubit states
• Strong Monogamy of Bipartite and Genuine Multipartite Entanglement: The Gaussian Case
• Quantifying quantum discord and entanglement of formation via unified purifications
• Experimental entanglement redistribution under decoherence channels
• Multipartite quantum correlation and entanglement in four-qubit pure states
• Multipartite entanglement in four-qubit cluster-class states
• Multipartite Entanglement Measure
• Strong superadditivity and monogamy of the Renyi measure of entanglement
• Are all maximally entangled states pure?
• Multipartite monogamy of the concurrence
• Possibility of generalized monogamy relations for multipartite entanglement beyond three qubits
• Entanglement in a class of multiqubit mixed states without multipartite tangles
• Entanglement evolution in multipartite cavity-reservoir systems under local unitary operations
• Entanglement evolution of three-qubit mixed states in multipartite cavity-reservoir systems
• Correlation evolution and monogamy of two geometric quantum discords in multipartite systems

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• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
• Monogamy of $\alpha$th Power Entanglement Measurement in Qubit Systems
• Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement
• Entanglement polygon inequality in qudit systems
• General Monogamy Relations of Quantum Entanglement for Multiqubit W-class States
• Conditions for monogamy of quantum correlations in multipartite systems
• Monogamy of quantum entanglement
• Forbidden regimes in the distribution of bipartite quantum correlations due to multiparty entanglement
• Resource conversion between operational coherence and multipartite entanglement in many-body systems
• Lower bounds on violation of monogamy inequality for quantum correlation measures
• Tightening monogamy and polygamy relations of unified entanglement in multipartite systems
• Long-range multipartite quantum correlations and factorization in a one-dimensional spin-1/2 $XY$ chain
• Generalized monogamy inequalities of convex-roof extended negativity in $N$-qubit systems
• Lower and upper bounds for entanglement of Rényi-$\alpha$ entropy
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• Realization of the tradeoff between internal and external entanglement
• Multi-linear Monogamy Relations for Three Qubit States
• Entanglement and measurement-induced nonlocality of mixed maximally entangled states in multipartite dynamics
• Maximum Violation of Monogamy of Entanglement for Indistinguishable Particles by Measures that are Monogamous for Distinguishable Particles
• Parameterized bipartite entanglement measures and entanglement constraints
• Tighter monogamy relations of entanglement measures based on fidelity
• Multipartite Monogamy of Entanglement for Three Qubit States
• Unified monogamy relations for the generalized $W$-class states beyond qubits
• Long-range bipartite entanglement in XXZ spin chains with the exponential and power-law long-range interactions