Why the results of solving ordinary differential equation get from ODE45 are not correct?

Recently, I make a program to solve Liouville von-neumann equation. The system Hamiltonian and initial state are known, I try to find the density matrix of system at any time.

The code as

    % define the function
      function dXdt = Liouvelle(t,X)
      % Delta=5;
      % epsilon=0.2;   % driving strength
      % Omega_d=10;    % driving frequency
      % Omega_r=10;   % frequency of cavity

    H=2*pi*[0.2 5; 5 -0.2];
    %H=2*pi*[Delta -epsilon*cos(2*pi*Omega_d*t);  -epsilon*cos(2*pi*Omega_d*t) -Delta]; %System Hamiltonian

     X = reshape(X, size(H)); 

    dXdt = -i*(H*X-X*H); %Liouville von-neumann equation
    dXdt = dXdt(:);

    % call the defined function to solve problem
    clear

    % initial state
    X2=[0.5 0.5;0.5 0.5];
    psi2=sqrt(2)/2*[1 1]';
    input=psi2;      
    %options = odeset('RelTol',1e-8,'AbsTol',1e-10);
    [T X]= ode45(@Liouvelle,[0:0.1:5],X2);

    [m n] = size(X);
    for j=1:m
       XX(:,:,j)=reshape(X(j,:),size(X2));

      F(j)=input'*XX(:,:,j)*input;         % Compute the fidelity, Nielsen 'quantum computation and
    % quantum information page 409 eq(9.60)

    end

    possibility=squeeze(XX(1,1,:));
    figure(2); plot(T,F); hold on;

However, I find the non-diag element of some density matrix is not correct because the product of the element are larger than 0.25. If I set precision at ode45, the results are improved but their product are still little bit larger than 0.25.

I don't know what's wrong and how to solve this problem.

Thanks.

Zhihui