% Number state filtered coherent state, NSFCS (Sec. II.F)
% A coherent state with one number state |m> removed from the superposition,
% then renormalized.

clear;          % Clear memory
clc;            % Clear the command window/screen
d = 15;
m = 4;          % number state |4> will be absent from the distribution
I = eye(d);
alpha = 0.8;    % amplitude of the coherent state
nsfs = 0;       % initialization
for x = 0:d-1
  if x == m
    nsfs = nsfs + 0*I(:,x+1);
  else
    nsfs = nsfs + exp(-norm(alpha)^2/2)*alpha^x/sqrt(prod(1:x))*I(:,x+1);
  end
end
NSFS = nsfs/norm(nsfs)   % normalize the state (note the 5th element is 0)