Unified monogamy and polygamy relations for multipartite systems

Abstract

For a bipartite entanglement measure $\mathcal{E}$ that satisfies the $\gamma$th-power monogamy inequality (Eq.~\eqref{e:chap1-ineq1}), and for its assisted counterpart ${\mathcal{E}}_a$ that obeys the $\delta$th-power polygamy inequality (Eq.~\eqref{e:chap1-ineq2}), we introduce a unified, tunable framework indexed by a parameter $m\ge 1$. Within this framework, we derive two hierarchical families of refined inequalities: a tightened $\alpha$-power monogamy relation for $\mathcal{E}$, valid for all $\alpha \ge m\gamma$; a tightened $\beta$-power polygamy relation for ${\mathcal{E}}_a$, applicable for $(m-1)\delta <\beta \le m\delta$. As $m$ increases, the bounds become progressively tighter, recovering known results at $m=1$. Notably, the optimal monogamy bound emerges as a piecewise function of $\alpha$, with additional correction terms activated as $\alpha$ crosses successive integer thresholds, thereby offering a sharper characterization of entanglement distribution. We demonstrate that our results generalize and strengthen existing monogamy and polygamy relations through analytical comparisons and numerical evaluations using concurrence and concurrence of assistance. This hierarchical, parameterized approach offers enhanced and flexible tools for applications in quantum communication, quantum networks, and multipartite quantum information processing.

14pp

References in corpus (30)

• Quantum entanglement
• Distributed Entanglement
• Universal state inversion and concurrence in arbitrary dimensions
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Substituting Quantum Entanglement for Communication
• Fidelity and Concurrence of conjugated states
• Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
• Concurrence of arbitrary dimensional bipartite quantum states
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Multipartite entanglement in three-mode Gaussian states of continuous variable systems: Quantification, sharing structure and decoherence
• Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
• Entanglement monogamy relations of qubit systems
• Duality for monogamy of entanglement
• Monogamy properties of quantum and classical correlations
• Deterministic Entanglement of Assistance and Monogamy Constraints
• Tighter monogamy relations in multipartite systems
• Entanglement Monogamy of Tripartite Quantum States
• Monogamy of entanglement without inequalities
• Negativity and strong monogamy of multi-party quantum entanglement beyond qubits
• Tighter entanglement monogamy relations of qubit systems
• Monogamy of entanglement and teleportation capability
• Bipartite entanglement in fermion systems
• Weighted polygamy inequalities of multiparty entanglement in arbitrary dimensional quantum systems
• Do Large Number of Parties Enforce Monogamy in All Quantum Correlations?
• Any entanglement of assistance is polygamous
• Tighter monogamy and polygamy relations of multiparty quantum entanglement
• General Monogamy and polygamy properties of quantum systems
• Tighter parameterized monogamy relations
• Superior monogamy and polygamy relations and estimates of concurrence