# On the no-signaling approach to quantum nonlocality

## Abstract

The no-signaling approach to nonlocality deals with separable and inseparable multiparty correlations in the same set of probability states without conflicting causality. The set of half-spaces describing the polytope of no-signaling probability states that are admitted by the most general class of Bell scenarios is formulated in full detail. An algorithm for determining the skeleton that solves the no-signaling description is developed upon a new strategy that is partially pivoting and partially incremental. The algorithm is formulated rigorously and its implementation is shown to be effective to deal with the highly degenerate no-signaling descriptions. Several applications of the algorithm as a tool for the study of quantum nonlocality are mentioned. Applied to a large set of bipartite Bell scenarios, we found that the corresponding no-signaling polytopes have a striking high degeneracy that grows up exponentially with the size of the Bell scenario.

- Authors:

- Instituto de Física, UASLP, San Luis Potosí, San Luis Potosí (Mexico)

- Publication Date:

- OSTI Identifier:
- 22403117

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CAUSALITY; CORRELATIONS; PROBABILITY

### Citation Formats

```
Méndez, J. M., E-mail: manolo@ifisica.uaslp.mx, and Urías, Jesús, E-mail: jurias@ifisica.uaslp.mx.
```*On the no-signaling approach to quantum nonlocality*. United States: N. p., 2015.
Web. doi:10.1063/1.4914336.

```
Méndez, J. M., E-mail: manolo@ifisica.uaslp.mx, & Urías, Jesús, E-mail: jurias@ifisica.uaslp.mx.
```*On the no-signaling approach to quantum nonlocality*. United States. doi:10.1063/1.4914336.

```
Méndez, J. M., E-mail: manolo@ifisica.uaslp.mx, and Urías, Jesús, E-mail: jurias@ifisica.uaslp.mx. Sun .
"On the no-signaling approach to quantum nonlocality". United States.
doi:10.1063/1.4914336.
```

```
@article{osti_22403117,
```

title = {On the no-signaling approach to quantum nonlocality},

author = {Méndez, J. M., E-mail: manolo@ifisica.uaslp.mx and Urías, Jesús, E-mail: jurias@ifisica.uaslp.mx},

abstractNote = {The no-signaling approach to nonlocality deals with separable and inseparable multiparty correlations in the same set of probability states without conflicting causality. The set of half-spaces describing the polytope of no-signaling probability states that are admitted by the most general class of Bell scenarios is formulated in full detail. An algorithm for determining the skeleton that solves the no-signaling description is developed upon a new strategy that is partially pivoting and partially incremental. The algorithm is formulated rigorously and its implementation is shown to be effective to deal with the highly degenerate no-signaling descriptions. Several applications of the algorithm as a tool for the study of quantum nonlocality are mentioned. Applied to a large set of bipartite Bell scenarios, we found that the corresponding no-signaling polytopes have a striking high degeneracy that grows up exponentially with the size of the Bell scenario.},

doi = {10.1063/1.4914336},

journal = {Journal of Mathematical Physics},

number = 3,

volume = 56,

place = {United States},

year = {Sun Mar 15 00:00:00 EDT 2015},

month = {Sun Mar 15 00:00:00 EDT 2015}

}