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.

12 pages, 6 figures

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Cited by in corpus (11)

• Entanglement polygon inequality in qudit systems
• General Monogamy Relations of Quantum Entanglement for Multiqubit W-class States
• Monogamy of quantum entanglement
• 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
• 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
• Long-range bipartite entanglement in XXZ spin chains with the exponential and power-law long-range interactions
• Unified monogamy relations for the generalized $W$-class states beyond qubits