toqito.states.gisin¶
Gisin states are the mixtures of separable mixed states and some purely entangled states.
Module Contents¶
- toqito.states.gisin.gisin(lambda_var, theta)[source]¶
Produce a Gisin state [@Gisin_1996_Hidden].
Returns the Gisin state described in [@Gisin_1996_Hidden]. Specifically, the Gisin state can be defined as:
- [
- begin{equation}
- rho_{lambda, theta} = lambda
- begin{pmatrix}
0 & 0 & 0 & 0 \ 0 & sin^2(theta) & -sin(theta)cos(theta) & 0 \ 0 & -sin(theta)cos(theta) & cos^2(theta) & 0 \ 0 & 0 & 0 & 0
end{pmatrix} + frac{1 - lambda}{2} begin{pmatrix}
1 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 1
end{pmatrix}.
end{equation}
]
Examples
The following code generates the Gisin state (rho_{0.5, 1}).
`python exec="1" source="above" from toqito.states import gisin print(gisin(0.5, 1)) `- Raises:
ValueError – If lambda_var is not a real number.
- Parameters:
lambda_var (float) – A real parameter in [0, 1].
theta (float) – A real parameter.
- Returns:
Gisin state.
- Return type:
numpy.ndarray