Weighted monogamy and polygamy relations

• URL: http://arxiv.org/abs/2402.14170v1
• Date: Wed, 21 Feb 2024 23:19:02 GMT
• Title: Weighted monogamy and polygamy relations
• Authors: Yue Cao, Naihuan Jing, Yiling Wang
• Abstract summary: 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.
• Score: 7.867858589759733
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This research offers a comprehensive approach to strengthening both monogamous and polygamous relationships within the context of quantum correlations in multipartite quantum systems. We present the most stringent bounds for both monogamy and polygamy in multipartite systems compared to recently established relations. 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.

Related papers

• General monogamy and polygamy relations of arbitrary quantum correlations for multipartite systems [0.0]
  General monogamy relations are presented for the $alpha$th $(0leqalpha leqgamma$, $gammageq2)$ power of quantum correlation. General polygamy relations are given for the $beta$th $(betageq delta$, $0leqdeltaleq1)$ power of quantum correlation.
  arXiv  Detail & Related papers  (2023-12-15T03:29:30Z)
• Polygamy relation of quantum correlations with equality [5.925000951196114]
  A polygamy relation with equality is given by introducing the polygamy weight. From the polygamy relation with equality, we present polygamy inequalities satisfied by the power of the quantum correlation measures.
  arXiv  Detail & Related papers  (2023-09-23T14:09:52Z)
• Multimodal Learning Without Labeled Multimodal Data: Guarantees and Applications [90.6849884683226]
  We study the challenge of interaction quantification in a semi-supervised setting with only labeled unimodal data. Using a precise information-theoretic definition of interactions, our key contribution is the derivation of lower and upper bounds. We show how these theoretical results can be used to estimate multimodal model performance, guide data collection, and select appropriate multimodal models for various tasks.
  arXiv  Detail & Related papers  (2023-06-07T15:44:53Z)
• On monogamy and polygamy relations of multipartite systems [9.730815192305782]
  We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems. It is known that any bipartite measure obeys monogamy and polygamy relations for the $r$-power of the measure.
  arXiv  Detail & Related papers  (2023-02-16T19:11:51Z)
• An Exponential Separation Between Quantum Query Complexity and the Polynomial Degree [79.43134049617873]
  In this paper, we demonstrate an exponential separation between exact degree and approximate quantum query for a partial function. For an alphabet size, we have a constant versus separation complexity.
  arXiv  Detail & Related papers  (2023-01-22T22:08:28Z)
• Tighter Constraints of Multipartite Systems in terms of General Quantum Correlations [0.0]
  We show that monogamy and polygamy relations are tighter than the existing ones. Taking concurrence and the Tsallis-$q$ entanglement of assistance as examples, we show the advantages of our results.
  arXiv  Detail & Related papers  (2022-02-04T17:33:16Z)
• Linguistic dependencies and statistical dependence [76.89273585568084]
  We use pretrained language models to estimate probabilities of words in context. We find that maximum-CPMI trees correspond to linguistic dependencies more often than trees extracted from non-contextual PMI estimate.
  arXiv  Detail & Related papers  (2021-04-18T02:43:37Z)
• Finite-Function-Encoding Quantum States [52.77024349608834]
  We introduce finite-function-encoding (FFE) states which encode arbitrary $d$-valued logic functions. We investigate some of their structural properties.
  arXiv  Detail & Related papers  (2020-12-01T13:53:23Z)
• 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)
• Complementary Quantum Correlations among Multipartite Systems [0.0]
  General monogamy relations are presented for the $alpha$th $(0leqalpha leqgamma, gammageq2)$ power of quantum correlation. General polygamy relations are given for the $beta$th $(betageq delta, 0leqdeltaleq1)$ power of quantum correlation.
  arXiv  Detail & Related papers  (2020-02-10T07:57:00Z)

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.