toqito.states.gisin

toqito.states.gisin(lambda_var, theta)

Produce a Gisin state [GIS96].

Returns the Gisin state described in [GIS96]. Specifically, the Gisin state can be defined as:

\[\begin{split}\begin{equation} \rho_{\lambda, \theta} = \lambda \begin{pmatrix} 0 & 0 & 0 & 0 \\ 0 & \sin^2(\theta) & -\sin(\theta)\cos(\theta) & 0 \\ 0 & -\sin(\theta)\cos(\theta) & \cos^2(\theta) & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix} + \frac{1 - \lambda}{2} \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}. \end{equation}\end{split}\]

Examples

The following code generates the Gisin state \(\rho_{0.5, 1}\).

>>> from toqito.states import gisin
>>> gisin(0.5, 1)
[[ 0.25      ,  0.        ,  0.        ,  0.        ],
 [ 0.        ,  0.35403671, -0.22732436,  0.        ],
 [ 0.        , -0.22732436,  0.14596329,  0.        ],
 [ 0.        ,  0.        ,  0.        ,  0.25      ]]

References

[GIS96] (1,2)

N. Gisin. Hidden quantum nonlocality revealed by local filters. (http://dx.doi.org/10.1016/S0375-9601(96)80001-6). 1996.

Raises:

ValueError – If lambda_var is not a real number.

Parameters:

• lambda_var – A real parameter in [0, 1].

• theta – A real parameter.

Returns:

Gisin state.