states.gisin

Gisin states are the mixtures of separable mixed states and some purely entangled states.

Functions

gisin(lambda_var, theta)

Produce a Gisin state [1].

Module Contents

states.gisin.gisin(lambda_var, theta)

Produce a Gisin state [1].

Returns the Gisin state described in [1]. 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)
array([[ 0.25      ,  0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.35403671, -0.22732436,  0.        ],
       [ 0.        , -0.22732436,  0.14596329,  0.        ],
       [ 0.        ,  0.        ,  0.        ,  0.25      ]])

References

[1] (1,2,3)

N. Gisin. Hidden quantum nonlocality revealed by local filters. Physics Letters A, 210(3):151–156, 1996. doi:https://doi.org/10.1016/S0375-9601(96)80001-6.

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