"Exercise 7.11 (Dr. W.Lindner)" "Calculate Alice's density matrix for sigma_z for the 'near-singlet' state." u = (1,0) d = (0,1) uu = (1,0,0,0) ud = (0,1,0,0) du = (0,0,1,0) dd = (0,0,0,1) -- "density matrix is rho_aa'= <a|psi><psi|a'> " -- wave function: -- uu ud du dd -- 1 2 3 4 psi = (0, sqrt(0.6), -sqrt(0.4), 0) "check normalized:" dot(psi,psi) "ok." "calculate ALICE's density matrix" "using rho_a'a = Sum( psi*(a,b).psi(a',b), b=uu,ud,du,dd)" rhouu = psi[1]*psi[1] + psi[2]*psi[2] rhouu rhoud = psi[3]*psi[1] + psi[4]*psi[2] rhoud rhodu = psi[1]*psi[3] + psi[2]*psi[4] rhodu rhodd = psi[3]*psi[3] + psi[4]*psi[4] rhodd "ALICE density matrix:" rhoAlice = ((rhouu,rhoud),(rhodu,rhodd)) rhoAlice rhoAlice^2 Tr(M)=contract(M) -- Tr = trace of matrix Tr(rhoAlice^2) Run