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 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