On Phi-entropic Dependence Measures and Non-local Correlations
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909525654634496 |
|---|---|
| author | Wang, Chenyu Gohari, Amin |
| author_facet | Wang, Chenyu Gohari, Amin |
| contents | We say that a measure of dependence between two random variables $X$ and $Y$, denoted as $ρ(X;Y)$, satisfies the data processing property if $ρ(X;Y)\geq ρ(X';Y')$ for every $X'\rightarrow X\rightarrow Y\rightarrow Y'$, and satisfies the tensorization property if $ρ(X_1X_2;Y_1Y_2)=\max\{ρ(X_1;Y_1),ρ(X_2;Y_2)\}$ when $(X_1,Y_1)$ is independent of $(X_2,Y_2)$. It is known that measures of dependence defined based on $Φ$-entropy satisfy these properties. These measures are important because they generalize R{é}nyi's maximal correlation and the hypercontractivity ribbon. The data processing and tensorization properties are special cases of monotonicity under wirings of non-local boxes. We show that ribbons defined using $Φ$-entropic measures of dependence are monotone under wiring of non-local no-signaling boxes, generalizing an earlier result. In addition, we also discuss the evaluation of $Φ$-strong data processing inequality constant for joint distributions obtained from a $Z$-channel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03754 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Phi-entropic Dependence Measures and Non-local Correlations Wang, Chenyu Gohari, Amin Information Theory We say that a measure of dependence between two random variables $X$ and $Y$, denoted as $ρ(X;Y)$, satisfies the data processing property if $ρ(X;Y)\geq ρ(X';Y')$ for every $X'\rightarrow X\rightarrow Y\rightarrow Y'$, and satisfies the tensorization property if $ρ(X_1X_2;Y_1Y_2)=\max\{ρ(X_1;Y_1),ρ(X_2;Y_2)\}$ when $(X_1,Y_1)$ is independent of $(X_2,Y_2)$. It is known that measures of dependence defined based on $Φ$-entropy satisfy these properties. These measures are important because they generalize R{é}nyi's maximal correlation and the hypercontractivity ribbon. The data processing and tensorization properties are special cases of monotonicity under wirings of non-local boxes. We show that ribbons defined using $Φ$-entropic measures of dependence are monotone under wiring of non-local no-signaling boxes, generalizing an earlier result. In addition, we also discuss the evaluation of $Φ$-strong data processing inequality constant for joint distributions obtained from a $Z$-channel. |
| title | On Phi-entropic Dependence Measures and Non-local Correlations |
| topic | Information Theory |
| url | https://arxiv.org/abs/2503.03754 |