# GisinState

 Other toolboxes required GisinState Produces a two-qubit Gisin state none 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 on "expand" to the right to view the MATLAB source code for this function.

1. %%  GISINSTATE    Produces a Gisin state
2. %   This function has two required input argument:
3. %     LAMBDA: A real parameter in [0,1].
4. %     THETA: A real parameter.
5. %
6. %   GISIN_STATE = GisinState(LAMBDA,THETA) returns the Gisin state
7. %   described in [1].
8. %
9. %   The Gisin states are a mixture of the entangled state rho_theta and the
10. %   separable states rho_uu and rho_dd.
11. %
12. %   References:
13. %   [1] N. Gisin. Hidden quantum nonlocality revealed by local filters.
14. %       (http://dx.doi.org/10.1016/S0375-9601(96)80001-6). 1996.
15. %
16. %   URL: http://www.qetlab.com/GisinState
17. 
18. %   requires: nothing
19. %   author: Vincent Russo (vrusso@uwaterloo.ca)
20. %   package: QETLAB
21. %   last updated: January 14, 2015
22. 
23. function gisin_state = GisinState( lambda, theta )
24. 
25. if lambda < 0 || lambda > 1
26.     error('GisinState:ImproperVal','LAMBDA must satisfy 0 <= LAMBDA <= 1.');
27. end
28. 
29. rho_theta = [ 0     0                0                0;
30.               0   sin(theta)^2      -sin(2*theta)/2 0;
31.               0   -sin(2*theta)/2   cos(theta)^2      0;
32.               0     0                0                0 ];
33. 
34. rho_uu_dd = [ 1 0 0 0;
35.               0 0 0 0;
36.               0 0 0 0;
37.               0 0 0 1 ];
38. 
39. gisin_state = lambda*rho_theta + (1-lambda)*rho_uu_dd/2;
40. 
41. end

## References

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