G_q-concurrence and entanglement constraints in multiqubit systems

• URL: http://arxiv.org/abs/2406.19080v1
• Date: Thu, 27 Jun 2024 11:07:51 GMT
• Title: G_q-concurrence and entanglement constraints in multiqubit systems
• Authors: Hui Li, Ting Gao, Fengli Yan,
• Abstract summary: 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.
• Score: 2.150800093140658
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we introduce a category of one-parameter bipartite entanglement quantifiers, termed $G_q$-concurrence ($q>1$), and show rigorously that they satisfy all the axiomatic conditions of an entanglement measure and can be considered as a generalization of concurrence. In addition, we establish an analytic formula relating $G_q$-concurrence to concurrence for $1<q\leq2$ in two-qubit systems. Furthermore, the polygamy relation is presented based on the $G_q$-concurrence of assistance in multiqubit systems. As far as $G_q$-concurrence ($1<q\leq2$) itself is concerned, however, it does not obey the monogamy relation, but we prove that the square of $G_q$-concurrence does. By means of this monogamy inequality, we construct a set of entanglement indicators that can detect genuinely multiqubit entangled states even when the tangle loses its efficacy.

Related papers

• 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)
• Entanglement hierarchies in multipartite scenarios [2.150800093140658]
  We present a whole set of hierarchical quantifications as a method of characterizing quantum states. We show that $k$-GM concurrence can unambiguously classify entangled states into $(n-1)$ distinct classes. In particular, $alpha$-$-GM concurrence $(0alpha1)$ determines that the GHZ state and the $W$ state belong to the same hierarchy.
  arXiv  Detail & Related papers  (2024-01-02T04:00:57Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• Parameterized multipartite entanglement measures [2.4172837625375]
  We present two types of entanglement measures in $n$-partite systems, $q$-$k$-ME concurrence $(qgeq2,2leq kleq n)$ and $alpha$-$k$-ME concurrence $(0leqalphaleqfrac12,2leq kleq n)$. Rigorous proofs show that the proposed $k$-nonseparable measures satisfy all the requirements for being an entanglement measure.
  arXiv  Detail & Related papers  (2023-08-31T01:58:47Z)
• Constructions of $k$-uniform states in heterogeneous systems [65.63939256159891]
  We present two general methods to construct $k$-uniform states in the heterogeneous systems for general $k$. We can produce many new $k$-uniform states such that the local dimension of each subsystem can be a prime power.
  arXiv  Detail & Related papers  (2023-05-22T06:58:16Z)
• 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)
• Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions [77.34726150561087]
  We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In particular, starting from a suitable quadratic form $Q$, the self-adjoint and bounded from below Hamiltonian $mathcal H$ can be constructed. We show that the threshold value $gamma_c$ is optimal, in the sense that the quadratic form $Q$ is unbounded from below if $gammagamma_c$.
  arXiv  Detail & Related papers  (2022-07-01T10:01:14Z)
• 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)
• Tighter constraints of multiqubit entanglement in terms of unified entropy [0.0]
  We present classes of monogamy inequalities related to the $alpha$-th ($alpha geq 1$) power of the entanglement measure based on the unified-($q,s$) entropy. We show that these monogamy and polygamy inequalities are tighter than the existing ones.
  arXiv  Detail & Related papers  (2021-10-22T03:11:11Z)
• Scattering data and bound states of a squeezed double-layer structure [77.34726150561087]
  A structure composed of two parallel homogeneous layers is studied in the limit as their widths $l_j$ and $l_j$, and the distance between them $r$ shrinks to zero simultaneously. The existence of non-trivial bound states is proven in the squeezing limit, including the particular example of the squeezed potential in the form of the derivative of Dirac's delta function. The scenario how a single bound state survives in the squeezed system from a finite number of bound states in the finite system is described in detail.
  arXiv  Detail & Related papers  (2020-11-23T14:40:27Z)
• Robustly Learning any Clusterable Mixture of Gaussians [55.41573600814391]
  We study the efficient learnability of high-dimensional Gaussian mixtures in the adversarial-robust setting. We provide an algorithm that learns the components of an $epsilon$-corrupted $k$-mixture within information theoretically near-optimal error proofs of $tildeO(epsilon)$. Our main technical contribution is a new robust identifiability proof clusters from a Gaussian mixture, which can be captured by the constant-degree Sum of Squares proof system.
  arXiv  Detail & Related papers  (2020-05-13T16:44:12Z)

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.