cubitt_RandomDensityMatrix.m

    %%  RANDOMDENSITYMATRIX    Generates a random density matrix
    % from http://www.qetlab.com/RandomDensityMatrix

    %   This function has one required argument:
    %     DIM: the number of rows (and columns) of the density matrix
    %
    %   RHO = RandomDensityMatrix(DIM) generates a random DIM-by-DIM density
    %   matrix, distributed according to the Hilbert-Schmidt measure.
    %
    %   This function has three optional arguments:
    %     RE (default 0)
    %     K (default DIM)
    %     DIST (default 'haar')
    %
    %   RHO = RandomDensityMatrix(DIM,RE,K,DIST) generates a random density
    %   matrix of rank <= K, distributed according to the distribution DIST. If
    %   RE = 1 then all of its entries will be real. DIST must be one of:
    %     'haar' or 'hs' (default) - Generate a larger  pure state according to
    %                      Haar measure and trace out the extra dimensions.
    %                      Sometimes called the Hilbert-Schmidt measure when
    %                      K = DIM.
    %     'bures'        - the Bures measure
    %
    %   URL: http://www.qetlab.com/RandomDensityMatrix
     
    %   requires: opt_args.m, RandomUnitary.m
    %
    %   author: Nathaniel Johnston (nathaniel@njohnston.ca)
    %   package: QETLAB
    %   last updated: October 10, 2014
     
    function rho = cubitt_RandomDensityMatrix(dim,varargin)
   
    % set optional argument defaults: re=0, k=dim, dist='hs'
    [re,k,dist] = opt_args({ 0, dim, 'haar' },varargin{:});
    
    % Haar/Hilbert-Schmidt measure
    gin = randn(dim,k);
    if(~re)
        gin = gin + 1i*randn(dim,k);
    end
    if(strcmpi(dist,'bures')) % Bures measure
        gin = (cubitt_randU(dim) + eye(dim))*gin;
    end
     
    rho = gin*gin';
    rho = rho/trace(rho);