On monogamy and polygamy relations of multipartite systems
- URL: http://arxiv.org/abs/2302.08534v1
- Date: Thu, 16 Feb 2023 19:11:51 GMT
- Title: On monogamy and polygamy relations of multipartite systems
- Authors: Xia Zhang, Naihuan Jing, Ming Liu, Haitao Ma
- Abstract summary: 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.
- Score: 9.730815192305782
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study the monogamy and polygamy relations related to quantum correlations
for multipartite quantum systems in a unified manner. It is known that any
bipartite measure obeys monogamy and polygamy relations for the $r$-power of
the measure. We show in a uniformed manner that the generalized monogamy and
polygamy relations are transitive to other powers of the measure in weighted
forms. We demonstrate that our weighted monogamy and polygamy relations are
stronger than recently available relations. Comparisons are given in detailed
examples which show that our results are stronger in both situations.
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) - 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) - Enriching Disentanglement: From Logical Definitions to Quantitative Metrics [59.12308034729482]
Disentangling the explanatory factors in complex data is a promising approach for data-efficient representation learning.
We establish relationships between logical definitions and quantitative metrics to derive theoretically grounded disentanglement metrics.
We empirically demonstrate the effectiveness of the proposed metrics by isolating different aspects of disentangled representations.
arXiv Detail & Related papers (2023-05-19T08:22:23Z) - 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) - Tighter monogamy and polygamy relations for a superposition of the
generalized $W$-class state and vacuum [0.0]
We investigate the monogamy and polygamy relations with respect to any partitions for a superposition of the generalized $W$-class state.
New classes of monogamy and polygamy inequalities are derived, which are shown to be tighter than the existing ones.
arXiv Detail & Related papers (2021-09-23T10:21:01Z) - 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) - MCMH: Learning Multi-Chain Multi-Hop Rules for Knowledge Graph Reasoning [46.68583750992613]
We consider a generalized form of multi-hop rules, where each rule is a set of relation chains.
We propose a two-step approach that first selects a small set of relation chains as a rule and then evaluates the confidence of the target relationship.
Empirical results show that our multi-chain multi-hop (MCMH) rules result in superior results compared to the standard single-chain approaches.
arXiv Detail & Related papers (2020-10-05T01:32:20Z)
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.