Tsallis entropy and entanglement constraints in multi-qubit systems

Abstract

We show that the restricted sharability and distribution of multi-qubit entanglement can be characterized by Tsallis-$q$ entropy. We first provide a class of bipartite entanglement measures named Tsallis-$q$ entanglement, and provide its analytic formula in two-qubit systems for $1\le q\le 4$. For $2\le q\le 3$, we show a monogamy inequality of multi-qubit entanglement in terms of Tsallis-$q$ entanglement, and we also provide a polygamy inequality using Tsallis-$q$ entropy for $1\le q\le 2$ and $3\le q\le 4$.

8 pages, 2 figures

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Cited by in corpus (66)

• 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
• Negativity and strong monogamy of multi-party quantum entanglement beyond qubits
• Generalized entropic measures of quantum correlations
• Limitations to sharing entanglement
• Monogamy of the Entanglement of Formation
• General polygamy inequality of multi-party quantum entanglement
• The Lambert-Tsallis Wq Function
• 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
• Any entanglement of assistance is polygamous
• Entanglement polygon inequality in qudit systems
• Parameterized multipartite entanglement measures
• Finer Distribution of Quantum Correlations among Multiqubit Systems
• Monogamy relations for generalized W class states in terms of Tsallis entropy beyond qubits
• Entanglement estimation in tensor network states via sampling
• Complementary Quantum Correlations among Multipartite Systems
• Quantum Correlation with Sandwiched Relative Entropies: Advantageous as Order Parameter in Quantum Phase Transitions
• Unification of multi-qubit polygamy inequalities
• Strong monogamy of multi-party quantum entanglement for partially coherently superposed states
• Parameterized Bipartite Entanglement Measure
• Monogamy of quantum entanglement
• Tighter monogamy and polygamy relations of multiparty quantum entanglement
• Symmetric generalized binomial distributions
• Strict entanglement monotonicity under local operations and classical communication
• Tightening monogamy and polygamy relations of unified entanglement in multipartite systems
• Tighter constraints of multiqubit entanglement in terms of Rényi-$\alpha$ entropy
• Entanglement of formation and monogamy of multi-party quantum entanglement
• On monogamy and polygamy relations of multipartite systems
• Estimating Parameterized Entanglement Measure
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• An Extention of Entanglement Measures for Pure States
• Polygamy relations of multipartite systems
• Tighter constraints of multiqubit entanglement in terms of unified entropy
• Monogamy and polygamy relations of quantum correlations for multipartite systems
• Tighter monogamy and polygamy relations of quantum entanglement in multi-qubit systems
• Monogamy of Entanglement Measures Based on Fidelity in Multiqubit Systems
• Monogamy of Logarithmic Negativity and Logarithmic Convex-Roof Extended Negativity
• Complete Genuine Multipartite Entanglement Monotone
• Tsallis entropy, $q$-expectation and constraints on three-party quantum correlations
• Tighter monogamy and polygamy relations for a superposition of the generalized $W$-class state and vacuum
• Tighter generalized monogamy and polygamy relations for multiqubit systems
• Polygamy relations of multipartite entanglement beyond qubits
• Partial-Norm of Entanglement: Entanglement Monotones That are not Monogamous
• Tighter constraints of multiqubit entanglement for negativity
• A new entanglement measure based on the total concurrence
• 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
• Strong polygamy of quantum correlations in multi-party quantum systems
• Maximum Violation of Monogamy of Entanglement for Indistinguishable Particles by Measures that are Monogamous for Distinguishable Particles
• General monogamy relations of the $S^t$ and $T_q^t$-entropy entanglement measures based on dual entropy
• Weighted monogamy and polygamy relations
• Tighter monogamy relations of entanglement measures based on fidelity
• Multipartite entanglement measures based on the thermodynamic framework
• Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA
• Parameterized bipartite entanglement measures and entanglement constraints
• Entanglement hierarchies in multipartite scenarios
• Tighter Constraints of Multipartite Systems in terms of General Quantum Correlations
• Classification of three-qubit genuine entangled states using concurrence fill
• Multipartite Monogamy of Entanglement for Three Qubit States
• Tighter bounds for generalized monogamy and polygamy relations
• Unified monogamy relation of entanglement measures
• Monogamy and polygamy for multi-qudit generalized $W$-class states based on concurrence of assistance and Tsallis-$q$ entanglement of assistance