GisinState

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 , 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

18. %   requires: nothing

19. %   author: Vincent Russo (vrusso@uwaterloo.ca)

20. %   package: QETLAB 

21. %   last updated: January 14, 2015

23. function gisin_state = GisinState( lambda, theta )

25. if lambda < 0 || lambda > 1

26.     error('GisinState:ImproperVal','LAMBDA must satisfy 0 <= LAMBDA <= 1.');

27. end

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 ];

34. rho_uu_dd = [ 1 0 0 0;

35.               0 0 0 0;

36.               0 0 0 0;

37.               0 0 0 1 ];

39. gisin_state = lambda*rho_theta + (1-lambda)*rho_uu_dd/2;

41. end