Monogamy relations and upper bounds for the generalized $W$-class states using R\'{e}nyi-$\alpha$ entropy

• URL: http://arxiv.org/abs/2010.16311v1
• Date: Thu, 30 Apr 2020 09:27:40 GMT
• Title: Monogamy relations and upper bounds for the generalized $W$-class states using R\'{e}nyi-$\alpha$ entropy
• Authors: Yanying Liang, Zhu-Jun Zheng, Chuan-Jie Zhu
• Abstract summary: We investigate monogamy relations and upper bounds for generalized $W$-class states related to the R'enyi-$alpha$ entropy. We apply our results into quantum games and present a new bound of the nonclassicality of quantum games restricting to generalized $W$-class states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Parameterized bipartite entanglement measures and entanglement constraints [1.125136513287558]
  We prove a novel class of parameterized entanglement measures which are named as $G_omega$-concurrence ($G_omega$C) We also prove a new polygamy relation of multiqubit quantum entanglement in terms of $G_omega$-concurrence of assistance ($G_omega$CoA) Based on the monogamy properties of S$G_omega$C, we can construct the corresponding multipartite entanglement indicators, which can detect all genuine multiqubit entangled states even in the case of $N$-tangle vanishes.
  arXiv  Detail & Related papers  (2025-03-18T13:32:21Z)
• Superior monogamy and polygamy relations and estimates of concurrence [6.408200192709026]
  We present a class of tighter parameterized monogamy relation for the $alpha$th $(alphageqgamma)$ power based on Eq. (1.1) This study provides a family of tighter lower (resp. upper) bounds of the monogamy (resp. polygamy) relations in a unified manner.
  arXiv  Detail & Related papers  (2025-03-02T02:25:34Z)
• Monogamy and polygamy for multi-qudit generalized $W$-class states based on concurrence of assistance and Tsallis-$q$ entanglement of assistance [1.125136513287558]
  We present new analytical monogamy inequalities satisfied by the $alpha$-th ($alphageqgamma,gammageq2$) power. We also establish new monogamy and polygamy relations, which are shown to be valid even for multipartite higher-dimensional states.
  arXiv  Detail & Related papers  (2025-02-17T07:56:06Z)
• Unified monogamy relations for the generalized $W$-class states beyond qubits [1.125136513287558]
  We study monogamy relations with respect to partitions for the generalized $W$-class (GW) states based on the unified-($q,s$) entanglement (UE) We provide the monogamy relation based on the squared UE for a reduced density matrix of a qudit GW state, as well as tighter monogamy relations based on the $alpha$th ($alphageq2$) power of UE.
  arXiv  Detail & Related papers  (2024-11-16T08:44:50Z)
• General monogamy relations of the $S^{t}$ and $T^{t}_q$-entropy entanglement measures based on dual entropy [0.0]
  We show that newly derived monogamy inequalities are tighter than the existing ones. Based on these general monogamy relations, we construct the set of multipartite entanglement indicators for $N$-qubit states.
  arXiv  Detail & Related papers  (2024-07-18T09:49:38Z)
• G_q-concurrence and entanglement constraints in multiqubit systems [2.150800093140658]
  We show that $G_q$-concurrence satisfies all the axiomatic conditions of an entanglement measure and can be considered as a generalization of concurrence. We construct a set of entanglement indicators that can detect genuinely multiqubit entangled states even when the tangle loses its efficacy.
  arXiv  Detail & Related papers  (2024-06-27T11:07:51Z)
• Dimension-free Remez Inequalities and norm designs [48.5897526636987]
  A class of domains $X$ and test sets $Y$ -- termed emphnorm -- enjoy dimension-free Remez-type estimates. We show that the supremum of $f$ does not increase by more than $mathcalO(log K)2d$ when $f$ is extended to the polytorus.
  arXiv  Detail & Related papers  (2023-10-11T22:46:09Z)
• Algebraic Aspects of Boundaries in the Kitaev Quantum Double Model [77.34726150561087]
  We provide a systematic treatment of boundaries based on subgroups $Ksubseteq G$ with the Kitaev quantum double $D(G)$ model in the bulk. The boundary sites are representations of a $*$-subalgebra $Xisubseteq D(G)$ and we explicate its structure as a strong $*$-quasi-Hopf algebra. As an application of our treatment, we study patches with boundaries based on $K=G$ horizontally and $K=e$ vertically and show how these could be used in a quantum computer
  arXiv  Detail & Related papers  (2022-08-12T15:05:07Z)
• Monogamy of entanglement between cones [68.8204255655161]
  We show that monogamy is not only a feature of quantum theory, but that it characterizes the minimal tensor product of general pairs of convex cones. Our proof makes use of a new characterization of products of simplices up to affine equivalence.
  arXiv  Detail & Related papers  (2022-06-23T16:23:59Z)
• Tightening monogamy and polygamy relations of unified entanglement in multipartite systems [1.6353216381658506]
  We first derive the monogamy inequality of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition. We then obtain the monogamy inequalities of the $alpha$th ($0leqalphaleqfracr2, rgeqsqrt2$) power of entanglement of formation for tripartite states.
  arXiv  Detail & Related papers  (2022-05-12T23:27:16Z)
• Simplest non-additive measures of quantum resources [77.34726150561087]
  We study measures that can be described by $cal E(rhootimes N) =E(e;N) ne Ne$.
  arXiv  Detail & Related papers  (2021-06-23T20:27:04Z)
• Improved Sample Complexity for Incremental Autonomous Exploration in MDPs [132.88757893161699]
  We learn the set of $epsilon$-optimal goal-conditioned policies attaining all states that are incrementally reachable within $L$ steps. DisCo is the first algorithm that can return an $epsilon/c_min$-optimal policy for any cost-sensitive shortest-path problem.
  arXiv  Detail & Related papers  (2020-12-29T14:06:09Z)
• An Optimal Separation of Randomized and Quantum Query Complexity [67.19751155411075]
  We prove that for every decision tree, the absolute values of the Fourier coefficients of a given order $ellsqrtbinomdell (1+log n)ell-1,$ sum to at most $cellsqrtbinomdell (1+log n)ell-1,$ where $n$ is the number of variables, $d$ is the tree depth, and $c>0$ is an absolute constant.
  arXiv  Detail & Related papers  (2020-08-24T06:50:57Z)
• Tighter constraints of multiqubit entanglement in terms of R\'{e}nyi-$\alpha$ entropy [5.316931601243777]
  monogamy and polygamy relations characterize the entanglement distributions in the multipartite systems. We present a class of monogamy inequalities related to the $mu$th power of the entanglement measure. These monogamy and polygamy relations are shown to be tighter than the existing ones.
  arXiv  Detail & Related papers  (2020-06-16T01:05:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.