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