Related papers: Tighter parameterized monogamy relations

Tighter parameterized monogamy relations

URL: http://arxiv.org/abs/2407.18127v1
Date: Thu, 25 Jul 2024 15:34:49 GMT
Title: Tighter parameterized monogamy relations
Authors: Yue Cao, Naihuan Jing, Kailash Misra, Yiling Wang,
Abstract summary: We seek a systematic tightening method to represent the monogamy relation for some measure in multipartite quantum systems. By introducing a family of parametrized bounds, we obtain tighter lowering bounds for the monogamy relation compared with the most recently discovered relations.
Score: 6.408200192709026
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We seek a systematic tightening method to represent the monogamy relation for some measure in multipartite quantum systems. By introducing a family of parametrized bounds, we obtain tighter lowering bounds for the monogamy relation compared with the most recently discovered relations. We provide detailed examples to illustrate why our bounds are better.

Related papers

Weighted monogamy and polygamy relations [7.867858589759733]
We show that whenever a bound is given (named it monogamy or polygamy) our bound indexed by some parameter $s$ will always be stronger than the given bound derived from the base relation. The study includes detailed examples, highlighting that our findings exhibit greater strength across all existing cases in comparison.
arXiv Detail & Related papers (2024-02-21T23:19:02Z)
Closing the Gap Between the Upper Bound and the Lower Bound of Adam's Iteration Complexity [51.96093077151991]
We derive a new convergence guarantee of Adam, with only an $L$-smooth condition and a bounded noise variance assumption. Our proof utilizes novel techniques to handle the entanglement between momentum and adaptive learning rate.
arXiv Detail & Related papers (2023-10-27T09:16:58Z)
Tighter monogamy relations in multiparty quantum systems [3.3986886334340616]
We investigate tight monogamy relations of multiparty quantum entanglement for any quantum state. We establish a class of tighter monogamy relations in tripartite quantum systems by means of the new inequality.
arXiv Detail & Related papers (2022-05-24T11:15:25Z)
Tighter monogamy and polygamy relations of quantum entanglement in multi-qubit systems [0.0]
We investigate the monogamy relations related to the concurrence, the entanglement of formation, convex-roof extended negativity, Tsallis-q entanglement and R'enyi-alpha entanglement. Monogamy and polygamy inequalities are obtained for arbitrary multipartite qubit systems, which are proved to be tighter than the existing ones.
arXiv Detail & Related papers (2021-12-31T12:37:55Z)
Tighter monogamy relations for the Tsallis-q and R\'{e}nyi-$\alpha$ entanglement in multiqubit systems [7.649038921524315]
We present some tighter monogamy relations in terms of the power of the Tsallis-q and R'enyi-$alpha$ entanglement in multipartite systems.
arXiv Detail & Related papers (2021-11-24T09:37:29Z)
Minibatch vs Local SGD with Shuffling: Tight Convergence Bounds and Beyond [63.59034509960994]
We study shuffling-based variants: minibatch and local Random Reshuffling, which draw gradients without replacement. For smooth functions satisfying the Polyak-Lojasiewicz condition, we obtain convergence bounds which show that these shuffling-based variants converge faster than their with-replacement counterparts. We propose an algorithmic modification called synchronized shuffling that leads to convergence rates faster than our lower bounds in near-homogeneous settings.
arXiv Detail & Related papers (2021-10-20T02:25:25Z)
Tighter Monogamy Relations in Multi-Qubit Systems [7.649038921524315]
We present some monogamy relations of multiqubit quantum entanglement in terms of the beta th power of concurrence, entanglement of formation and convex-roof extended negativity. These monogamy relations are proved to be tighter than the existing ones, together with detailed examples showing the tightness.
arXiv Detail & Related papers (2021-10-13T09:15:59Z)
R\'enyi divergence inequalities via interpolation, with applications to generalised entropic uncertainty relations [91.3755431537592]
We investigate quantum R'enyi entropic quantities, specifically those derived from'sandwiched' divergence. We present R'enyi mutual information decomposition rules, a new approach to the R'enyi conditional entropy tripartite chain rules and a more general bipartite comparison.
arXiv Detail & Related papers (2021-06-19T04:06:23Z)
Relative Deviation Margin Bounds [55.22251993239944]
We give two types of learning bounds, both distribution-dependent and valid for general families, in terms of the Rademacher complexity. We derive distribution-dependent generalization bounds for unbounded loss functions under the assumption of a finite moment.
arXiv Detail & Related papers (2020-06-26T12:37:17Z)
Lower bounds in multiple testing: A framework based on derandomized proxies [107.69746750639584]
This paper introduces an analysis strategy based on derandomization, illustrated by applications to various concrete models. We provide numerical simulations of some of these lower bounds, and show a close relation to the actual performance of the Benjamini-Hochberg (BH) algorithm.
arXiv Detail & Related papers (2020-05-07T19:59:51Z)
Tight Lower Bounds for Combinatorial Multi-Armed Bandits [72.56064196252498]
The Combinatorial Multi-Armed Bandit problem is a sequential decision-making problem in which an agent selects a set of arms on each round. We show that the recently proposed Gini-weighted smoothness parameter determines the lower bounds for monotone reward functions.
arXiv Detail & Related papers (2020-02-13T08:53:43Z)

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