Parameterized multipartite entanglement measures

• URL: http://arxiv.org/abs/2308.16393v1
• Date: Thu, 31 Aug 2023 01:58:47 GMT
• Title: Parameterized multipartite entanglement measures
• Authors: Hui Li, Ting Gao, Fengli Yan
• Abstract summary: 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.
• Score: 2.4172837625375
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate parameterized multipartite entanglement measures from the perspective of $k$-nonseparability in this paper. We present two types of entanglement measures in $n$-partite systems, $q$-$k$-ME concurrence $(q\geq2,~2\leq k\leq n)$ and $\alpha$-$k$-ME concurrence $(0\leq\alpha\leq\frac{1}{2},~2\leq k\leq n)$, which unambiguously detect all $k$-nonseparable states in arbitrary $n$-partite systems. Rigorous proofs show that the proposed $k$-nonseparable measures satisfy all the requirements for being an entanglement measure including the entanglement monotone, strong monotone, convexity, vanishing on all $k$-separable states, and being strictly greater than zero for all $k$-nonseparable states. In particular, the $q$-2-ME concurrence and $\alpha$-2-ME concurrence, renamed as $q$-GME concurrence and $\alpha$-GME concurrence, respectively, are two kinds of genuine entanglement measures corresponding the case where the systems are divided into bipartition $(k=2)$. The lower bounds of two classes $k$-nonseparable measures are obtained by employing the approach that takes into account the permutationally invariant part of a quantum state. And the relations between $q$-$n$-ME concurrence ($\alpha$-$n$-ME concurrence) and global negativity are established. In addition, we discuss the degree of separability and elaborate on an effective detection method with concrete examples. Moreover, we compare the $q$-GME concurrence defined by us to other genuine entanglement measures.

Related papers

• 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)
• $su(d)$-squeezing and many-body entanglement geometry in finite-dimensional systems [0.0]
  Generalizing the well-known spin-squeezing inequalities, we study the relation between squeezing of collective $N$-particle $su(d)$ operators and many-body entanglement geometry in multi-particle systems.
  arXiv  Detail & Related papers  (2024-06-19T08:40:11Z)
• Quantifying multipartite quantum states by ($k+1$)-partite entanglement measures [2.150800093140658]
  We put forward two families of entanglement measures termed $q$-$(k+1)$-PE concurrence $(q>1)$ and $alpha$-$(k+1)$-PE concurrence $(0leqalpha1)$. We also propose two alternative kinds of entanglement measures, named $q$-$(k+1)$-GPE concurrence $(q>1)$ and $alpha$-$(k+1)$-GPE concurrence $(0leqalpha1)$.
  arXiv  Detail & Related papers  (2024-04-23T13:19:17Z)
• Mixed-state quantum anomaly and multipartite entanglement [8.070164241593814]
  We show a surprising connection between mixed state entanglement and 't Hooft anomaly. We generate examples of mixed states with nontrivial long-ranged multipartite entanglement. We also briefly discuss mixed anomaly involving both strong and weak symmetries.
  arXiv  Detail & Related papers  (2024-01-30T19:00:02Z)
• 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)
• Combinatorial Stochastic-Greedy Bandit [79.1700188160944]
  We propose a novelgreedy bandit (SGB) algorithm for multi-armed bandit problems when no extra information other than the joint reward of the selected set of $n$ arms at each time $tin [T]$ is observed. SGB adopts an optimized-explore-then-commit approach and is specifically designed for scenarios with a large set of base arms.
  arXiv  Detail & Related papers  (2023-12-13T11:08:25Z)
• 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)
• Contextual Combinatorial Bandits with Probabilistically Triggered Arms [55.9237004478033]
  We study contextual bandits with probabilistically triggered arms (C$2$MAB-T) under a variety of smoothness conditions. Under the triggering modulated (TPM) condition, we devise the C$2$-UC-T algorithm and derive a regret bound $tildeO(dsqrtT)$.
  arXiv  Detail & Related papers  (2023-03-30T02:51:00Z)
• 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)
• Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
  Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
  arXiv  Detail & Related papers  (2020-06-04T17:51:00Z)
• 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.