GisinState

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GisinState
Produces a two-qubit Gisin state

Other toolboxes required none
Function category Special states, vectors, and operators

GisinState is a function that produces a two-qubit "Gisin state", as defined in [1], which has the following standard basis representation: \[\rho_{\lambda,\theta} := \lambda\begin{bmatrix}0 & 0 & 0 & 0 \\ 0 & \sin^2(\theta) & -\sin(\theta)\cos(\theta) & 0 \\ 0 & -\sin(\theta)\cos(\theta) & \cos^2(\theta) & 0 \\ 0 & 0 & 0 & 0\end{bmatrix} + \frac{1-\lambda}{2}\begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1\end{bmatrix}.\]

Syntax

  • GISIN_STATE = GisinState(LAMBDA,THETA)

Argument descriptions

  • LAMBDA: A real number between 0 and 1.
  • THETA: A real number.

Examples

The following code generates the Gisin state $\rho_{0.5,1}$:

>> GisinState(0.5,1)

ans =

    0.2500         0         0         0
         0    0.3540   -0.2273         0
         0   -0.2273    0.1460         0
         0         0         0    0.2500

Source code

Click here to view this function's source code on github.

References

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