% example_optwitness Example for the application of example_optwitness % We look for a witness for a six-qubit symmetric Dicke state % Used in http://arxiv.org/abs/0903.3910. echo on % Looking for maximum for Jx^2+Jy^2 for states that are biseparable % with respect to some bipartition of the qubits % Number of quibits (2..6) N=6; % N-qubit symmetric Dicke state with N/2 excitations rho=ketbra(dstate(N/2,N)); % White noise rho_noise=mmstate(N); % Projector-based witness witness_proj=N/(N-1)/2*qeye(N)-rho; % Define Pauli spin matrices x,y,z and e paulixyz; % Define the collective angular momentum components Jx=coll(x,N)/2; Jy=coll(y,N)/2; Jz=coll(z,N)/2; % Look for a witness as a linear combination of the followin operators op_array=[qeye(N) Jx^2 Jx^4 Jx^6 Jy^2 Jy^4 Jy^6 Jz^2 Jz^4 Jz^6]; % Determine optimal witness [W_opt,alpha,coeff]=optwitness(rho,rho_noise,witness_proj,op_array); echo off