GisinState
From QETLAB
GisinState | |
Produces a two-qubit Gisin state | |
Other toolboxes required | none |
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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.
%% GISINSTATE Produces a Gisin state
% This function has two required input argument:
% LAMBDA: A real parameter in [0,1].
% THETA: A real parameter.
%
% GISIN_STATE = GisinState(LAMBDA,THETA) returns the Gisin state
% described in [1].
%
% The Gisin states are a mixture of the entangled state rho_theta and the
% separable states rho_uu and rho_dd.
%
% References:
% [1] N. Gisin. Hidden quantum nonlocality revealed by local filters.
% (http://dx.doi.org/10.1016/S0375-9601(96)80001-6). 1996.
%
% URL: http://www.qetlab.com/GisinState
% requires: nothing
% author: Vincent Russo (vrusso@uwaterloo.ca)
% package: QETLAB
% last updated: January 14, 2015
function gisin_state = GisinState( lambda, theta )
if lambda < 0 || lambda > 1
error('GisinState:ImproperVal','LAMBDA must satisfy 0 <= LAMBDA <= 1.');
end
rho_theta = [ 0 0 0 0;
0 sin(theta)^2 -sin(2*theta)/2 0;
0 -sin(2*theta)/2 cos(theta)^2 0;
0 0 0 0 ];
rho_uu_dd = [ 1 0 0 0;
0 0 0 0;
0 0 0 0;
0 0 0 1 ];
gisin_state = lambda*rho_theta + (1-lambda)*rho_uu_dd/2;
end
References
- ↑ N. Gisin. Hidden quantum nonlocality revealed by local filters. 1996. doi:10.1016/S0375-9601(96)80001-6