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Register a new userMonogamy relation of multi-qubit systems for squared Tsallis-emph{q} entanglement
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Tsallis-$q$ entanglement is a bipartite entanglement measure which is the generalization of entanglement of formation for $q$ tending to 1. We first expand the range of $q$ for the analytic formula of Tsallis-emph{q} entanglement. For $frac{5-sqrt{13}}{2} leq emph{q} leq frac{5+sqrt{13}}{2}$, we prove the monogamy relation in terms of the squared Tsallis-$q$ entanglement for an arbitrary multi-qubit systems. It is shown that the multipartite entanglement indicator based on squared Tsallis-$q$ entanglement still works well even when the indicator based on the squared concurrence loses its efficacy. We also show that the $mu$-th power of Tsallis-emph{q} entanglement satisfies the monogamy or polygamy inequalities for any three-qubit state.
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In this paper, we study the monogamy inequality of Tsallis-q entropy entanglement. We first provide an analytic formula of Tsallis-q entropy entanglement in two-qubit systems for $frac{5-sqrt{13}}{2}leq qleqfrac{5+sqrt{13}}{2}.$ The analytic formula of Tsallis-q entropy entanglement in $2otimes d$ system is also obtained and we show that Tsallis-q entropy entanglement satisfies a set of hierarchical monogamy equalities. Furthermore, we prove the squared Tsallis-q entropy entanglement follows a general inequality in the qubit systems. Based on the monogamy relations, a set of multipartite entanglement indicators is constructed, which can detect all genuine multiqubit entangled states even in the case of $N$-tangle vanishes. Moreover, we study some examples in multipartite higher-dimensional system for the monogamy inequalities.
We investigate the monogamy relations related to the concurrence and the entanglement of formation. General monogamy inequalities given by the {alpha}th power of concurrence and entanglement of formation are presented for N-qubit states. The monogamy relation for entanglement of assistance is also established. Based on these general monogamy relations, the residual entanglement of concurrence and entanglement of formation are studied. Some relations among the residual entanglement, entanglement of assistance, and three tangle are also presented.
The quantum steering ellipsoid can be used to visualise two-qubit states, and thus provides a generalisation of the Bloch picture for the single qubit. Recently, a monogamy relation for the volumes of steering ellipsoids has been derived for pure 3-qubit states and shown to be stronger than the celebrated Coffman-Kundu-Wootters (CKW) inequality. We first demonstrate the close connection between this volume monogamy relation and the classification of pure 3-qubit states under stochastic local operations and classical communication (SLOCC). We then show that this monogamy relation does not hold for general mixed 3-qubit states and derive a weaker monogamy relation that does hold for such states. We also prove a volume monogamy relation for pure 4-qubit states, and generalize our 3-qubit inequality to n qubits. Finally, we study the effect of noise on the quantum steering ellipsoid and find that the volume of any two-qubit state is non-increasing when the state is exposed to arbitrary local noise. This implies that any volume monogamy relation for a given class of multi-qubit states remains valid under the addition of local noise. We investigate this quantitatively for the experimentally relevant example of isotropic noise.
The monogamy of quantum entanglement captures the property of limitation in the distribution of entanglement. Various monogamy relations exist for different entanglement measures that are important in quantum information processing. Our goal in this work is to propose a general monogamy inequality for all entanglement measures on entangled qubit systems. The present result provide a unified model for various entanglement measures including the concurrence, the negativity, the entanglement of formation, Tsallis-q entropy, Renyi-q entropy, and Unified-(q,s) entropy. We then proposed tightened monogamy inequalities for multipartite systems. We finally prove a generic result for the tangle of high-dimensional entangled states to show the distinct feature going beyond qubit systems. These results are useful for exploring the entanglement theory, quantum information processing and secure quantum communication.
We prove a new polygamy relation of multi-party quantum entanglement in terms of R{e}nyi-$alpha$ entanglement of assistance for $left( {sqrt 7 - 1} right)/2leqalpha leq left( {sqrt 13 - 1} right)/2$. This class of polygamy inequality reduces to the polygamy inequality based on entanglement of assistance since R{e}nyi-$alpha$ entanglement is a generalization of entanglement of formation. We further show that the polygamy inequality also holds for the $mu$th power of R{e}nyi-$alpha$ entanglement of assistance.
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