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Register a new userTighter monogamy and polygamy relations using R{e}nyi-$alpha$ entropy
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We investigate monogamy relations related to the R{e}nyi-$alpha$ entanglement and polygamy relations related to the R{e}nyi-$alpha$ entanglement of assistance. We present new entanglement monogamy relations satisfied by the $mu$-th power of R{e}nyi-$alpha$ entanglement with $alphain[sqrt{7}-1)/2,(sqrt{13}-1)/2]$ for $mugeqslant2$, and polygamy relations satisfied by the $mu$-th power of R{e}nyi-$alpha$ entanglement of assistance with $alphain[sqrt{7}-1)/2,(sqrt{13}-1)/2]$ for $0leqmuleq1$. These relations are shown to be tighter than the existing ones.
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We investigate monogamy relations and upper bounds for generalized $W$-class states related to the R{e}nyi-$alpha$ entropy. First, we present an analytical formula on R{e}nyi-$alpha$ entanglement (R$alpha$E) and R{e}nyi-$alpha$ entanglement of assistance (REoA) of a reduced density matrix for a generalized $W$-class states. According to the analytical formula, we show monogamy and polygamy relations for generalized $W$-class states in terms of R$alpha$E and REoA. Then we give the upper bounds for generalized $W$-class states in terms of R$alpha$E. Next, we provide tighter monogamy relations for generalized $W$-class states in terms of concurrence and convex-roof extended negativity and obtain the monogamy relations for R$alpha$E by the analytical expression between R$alpha$E and concurrence. Finally, we apply our results into quantum games and present a new bound of the nonclassicality of quantum games restricting to generalized $W$-class states.
The resource theories of quantum coherence attract a lot of attention in recent years. Especially, the monotonicity property plays a crucial role here. In this paper we investigate the monotonicity property for the coherence measures induced by the R{e}nyi $alpha$-relative entropy which present in [Phys. Rev. A 94, 052336, 2016]. We show that the R{e}nyi $alpha$-relative entropy of coherence does not in general satisfy the monotonicity requirement under the subselection of measurements condition and it also does not satisfy the extension of monotonicity requirement which presents in [Phys. Rev. A 93, 032136, 2016]. Due to the R{e}nyi $alpha$-relative entropy of coherence can act as a coherence monotone quantifier, we examine the trade-off relations between coherence and mixedness. Finally, some properties for the single qubit of R{e}nyi $2$-relative entropy of coherence are derived.
In this work, we establish an exact relation which connects the heat exchange between two systems initialized in their thermodynamic equilibrium states at different temperatures and the R{e}nyi divergences between the initial thermodynamic equilibrium state and the final non-equilibrium state of the total system. The relation tells us that the various moments of the heat statistics are determined by the Renyi divergences between the initial equilibrium state and the final non-equilibrium state of the global system. In particular the average heat exchange is quantified by the relative entropy between the initial equilibrium state and the final non-equilibrium state of the global system. The relation is applicable to both finite classical systems and finite quantum systems.
The R{e}nyi and von Neumann entropies of various bipartite Gaussian states are derived analytically. We also discuss on the tripartite purification for the bipartite states when some particular conditions hold. The generalization to non-Gaussian states is briefly discussed.
We investigate possible generalizations of the Coffman-Kundu-Wootters monogamy inequality to four qubits, accounting for multipartite entanglement in addition to the bipartite terms. We show that the most natural extension of the inequality does not hold in general, and we describe the violations of this inequality in detail. We investigate alternative ways to extend the monogamy inequality to express a constraint on entanglement sharing valid for all four-qubit states, and perform an extensive numerical analysis of randomly generated four-qubit states to explore the properties of such extensions.
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