# Minimal keys for Bell Expressions¶

The simplest Bell expression is described by the following YAML fragment:

type: BellExpression
scenario: '[(2 2) (2 2)]'
representation: Non-signaling Correlators
coefficients: [0, 0, 0, 0, 1, -1, 0, 1, 1]


The following properties are always required:

type
The type of a Bell expression is always a string equal to BellExpression.
scenario
The String describing the scenario in which the expression is defined. The format of scenarios is detailed in Appendix A of arXiv.
For example, a scenario with two parties, two settings and two outcomes is specified by:
scenario: [(2 2) (2 2)]

representation
This key specifies the parametrization used for the Bell expression coefficients. The supported representations are detailed in Representations.
coefficients
Vector of integer or rational coefficients describing the Bell expression. In the case of integer coefficients, the value associated to the coefficients key is a YAML sequence of integers. In the case of rational coefficients, the value associated to the coefficients key is a mapping with numerator and denominator keys. The value associated to the numerator key is a sequence of integer, and denominator is a single integer acting as the common denominator of the coefficients.

Here are several examples of valid Bell expressions.

The CHSH inequality, written in the Collins-Gisin notation:

type: BellExpression
scenario: '[(2 2) (2 2)]'
representation: Non-signaling Collins-Gisin
coefficients: [0, -1, 0, -1, 1, 1, 0, 1, -1]


The Guess Your Neighbor’s Input inequality, written using full Probabilities:

type: BellExpression
scenario: '[(2 2) (2 2) (2 2)]'
representation: Signaling Probabilities
coefficients:
numerator: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
denominator: 4