Monogamy and polygamy for multi-qubit entanglement using Rényi entropy

Abstract

Using Rényi-$\alpha$ entropy to quantify bipartite entanglement, we prove monogamy of entanglement in multi-qubit systems for $\alpha \ge 2$. We also conjecture a polygamy inequality of multi-qubit entanglement with strong numerical evidence for $0.83-\epsilon \le \alpha \le 1.43+\epsilon$ with $0<\epsilon <0.01$.

19 pages, 2 figures

References in corpus (7)

• General Monogamy Inequality for Bipartite Qubit Entanglement
• Is Entanglement Monogamous?
• Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
• An elementary formula for entanglement entropies of fermionic systems
• Generalized W-Class State and its Monogamy Relation
• Generalized decoding, effective channels, and simplified security proofs in quantum key distribution
• Strong superadditivity and monogamy of the Renyi measure of entanglement

Cited by in corpus (61)

• Continuous variable quantum information: Gaussian states and beyond
• Non-Gaussian Quantum States and Where to Find Them
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Should Entanglement Measures be Monogamous or Faithful?
• General Monogamy of Tsallis $q$-Entropy Entanglement in Multiqubit Systems
• Tighter monogamy relations in multipartite systems
• Unified entropy, entanglement measures and monogamy of multi-party entanglement
• Monogamy of entanglement without inequalities
• Negativity and strong monogamy of multi-party quantum entanglement beyond qubits
• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
• Limitations to sharing entanglement
• Monogamy of the Entanglement of Formation
• Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems
• General polygamy inequality of multi-party quantum entanglement
• Entanglement Rényi $\alpha$-entropy
• Why the Entanglement of Formation is not generally monogamic
• Weighted polygamy inequalities of multiparty entanglement in arbitrary dimensional quantum systems
• A new parameterized entanglement monotone
• Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement
• Entanglement polygon inequality in qudit systems
• Exponentially many entanglement and correlation constraints for multipartite quantum states
• Finer Distribution of Quantum Correlations among Multiqubit Systems
• Generalized Entropy and Global Quantum Discord in Multi-party Quantum systems
• Unification of multi-qubit polygamy inequalities
• Parameterized Bipartite Entanglement Measure
• Strong monogamy of multi-party quantum entanglement for partially coherently superposed states
• Monogamy of quantum entanglement
• Strict entanglement monotonicity under local operations and classical communication
• Monogamy relations and upper bounds for the generalized $W$-class states using Rényi-$\alpha$ entropy
• Resource conversion between operational coherence and multipartite entanglement in many-body systems
• 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
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• Entanglement of formation and monogamy of multi-party quantum entanglement
• Realization of the tradeoff between internal and external entanglement
• Lower and upper bounds for entanglement of Rényi-$\alpha$ entropy
• Monogamy of Entanglement Measures Based on Fidelity in Multiqubit Systems
• Tighter monogamy and polygamy relations of quantum entanglement in multi-qubit systems
• Tighter constraints of multiqubit entanglement in terms of unified entropy
• Monogamy and polygamy relations of quantum correlations for multipartite systems
• Monogamy of Logarithmic Negativity and Logarithmic Convex-Roof Extended Negativity
• Tighter monogamy and polygamy relations for a superposition of the generalized $W$-class state and vacuum
• Condition on the Rényi Entanglement Entropy under Stochastic Local Manipulation
• Tsallis entropy, $q$-expectation and constraints on three-party quantum correlations
• Classification and measurement of multipartite entanglement by reconstruction of correlation tensors on an NMR quantum processor
• Complete Genuine Multipartite Entanglement Monotone
• Tighter constraints of multiqubit entanglement for negativity
• Tighter monogamy relations in multiparty quantum systems
• Polygamy of multi-party $q$-expected quantum entanglement
• Tighter weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems
• General monogamy relations of the $S^t$ and $T_q^t$-entropy entanglement measures based on dual entropy
• Maximum Violation of Monogamy of Entanglement for Indistinguishable Particles by Measures that are Monogamous for Distinguishable Particles
• Strong polygamy of quantum correlations in multi-party quantum systems
• Entanglement, loss, and quantumness: When balanced beam splitters are best
• Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA
• Transmission of coherent information at the onset of interactions
• Parameterized bipartite entanglement measures and entanglement constraints
• Tighter monogamy relations of entanglement measures based on fidelity
• Multipartite Monogamy of Entanglement for Three Qubit States
• Entanglement distribution in fermion model with long-range interaction
• Classification of three-qubit genuine entangled states using concurrence fill