The polygon relation and subadditivity of entropic measures for discrete
and continuous multipartite entanglement
- URL: http://arxiv.org/abs/2401.02066v1
- Date: Thu, 4 Jan 2024 05:09:37 GMT
- Title: The polygon relation and subadditivity of entropic measures for discrete
and continuous multipartite entanglement
- Authors: Lijun Liu, Xiaozhen Ge, and Shuming Cheng
- Abstract summary: We study the relationship between the polygon relation and the subadditivity of entropy.
Our work provides a better understanding of the rich structure of multipartite states.
- Score: 0.6759148939470331
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In a recent work [Ge {\it et al.}, arXiv: 2312. 17496 (2023)], we have
derived the polygon relation of bipartite entanglement measures that is useful
to reveal the entanglement properties of discrete, continuous, and even hybrid
multipartite quantum systems. In this work, with the information-theoretical
measures of R\'enyi and Tsallis entropies, we study the relationship between
the polygon relation and the subadditivity of entropy. In particular, the
entropy-polygon relations are derived for pure multi-qubit states and
generalized to multi-mode Gaussian states, by utilizing the known results from
the quantum marginal problem. Moreover, the equivalence between the polygon
relation and subadditivity is established, in the sense that for all discrete
or continuous multipartite states, the polygon relation holds if and only if
the underlying entropy is subadditive. As byproduct, the subadditivity of
R\'enyi and Tsallis entropies is proven for all bipartite Gaussian states.
Finally, the difference between polygon relations and monogamy relations is
clarified, and generalizations of our results are discussed. Our work provides
a better understanding of the rich structure of multipartite states, and hence
is expected to be helpful for the study of multipartite entanglement.
Related papers
- Gaussian Entanglement Measure: Applications to Multipartite Entanglement
of Graph States and Bosonic Field Theory [50.24983453990065]
An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers.
We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states.
By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
arXiv Detail & Related papers (2024-01-31T15:50:50Z) - Approximation of multipartite quantum states: revised version with new
applications [0.0]
We show that for any multipartite state with finite energy the infimum in the definition of the relative entropy of $pi$-entanglement can be taken over the set of finitely-decomposable $pi$-separable states with finite energy.
We also show that for any multipartite state with finite energy the infimum in the definition of the relative entropy of $pi$-entanglement can be taken over the set of finitely-decomposable $pi$-separable states with finite energy.
arXiv Detail & Related papers (2024-01-04T17:59:01Z) - Entanglement and entropy in multipartite systems: a useful approach [0.0]
We show how the notion of concurrence vector, re-expressed in a particularly useful form, provides new insights and computational tools.
The approach is also useful to derive sufficient conditions for genuine entanglement in generic multipartite systems.
arXiv Detail & Related papers (2023-07-11T12:20:30Z) - Revisiting Tropical Polynomial Division: Theory, Algorithms and
Application to Neural Networks [40.137069931650444]
Tropical geometry has recently found several applications in the analysis of neural networks with piecewise linear activation functions.
This paper presents a new look at the problem of tropical division and its application to the simplification of neural networks.
arXiv Detail & Related papers (2023-06-27T02:26:07Z) - Entanglement monogamy via multivariate trace inequalities [12.814476856584346]
We derive variational formulas for relative entropies based on restricted measurements of multipartite quantum systems.
We give direct, matrix-analysis-based proofs for the faithfulness of squashed entanglement.
arXiv Detail & Related papers (2023-04-28T14:36:54Z) - 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) - Multipartitioning topological phases by vertex states and quantum
entanglement [9.519248546806903]
We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three spatial regions.
We compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra.
As specific examples, we consider topological chiral $p$-wave superconductors and Chern insulators.
arXiv Detail & Related papers (2021-10-22T18:01:24Z) - 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) - Approximation of multipartite quantum states and the relative entropy of
entanglement [0.0]
We prove several results about analytical properties of the multipartite relative entropy of entanglement and its regularization.
We establish a finite-dimensional approximation property for the relative entropy of entanglement and its regularization.
arXiv Detail & Related papers (2021-03-22T18:12:24Z) - Long-distance entanglement of purification and reflected entropy in
conformal field theory [58.84597116744021]
We study entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy.
We find an elementary proof that the decay of both, the entanglement of purification and reflected entropy, is enhanced with respect to the mutual information behaviour.
arXiv Detail & Related papers (2021-01-29T19:00:03Z) - 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)
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.