"Exercise 6.8" u = (1,0) d = (0,1) uu = kronecker(u,u) ud = kronecker(u,d) du = kronecker(d,u) dd = kronecker(d,d) sigmaz = ((1,0),(0,-1)) sigmax = ((0,1),(1,0)) sigmay = ((0,-i),(i,0)) tauz = ((1,0),(0,-1)) taux = ((0,1),(1,0)) tauy = ((0,-i),(i,0)) I = ((1,0),(0,1)) sigmaz = kronecker(sigmaz,I) sigmax = kronecker(sigmax,I) sigmay = kronecker(sigmay,I) tauz = kronecker(I,tauz) taux = kronecker(I,taux) tauy = kronecker(I,tauy) T2 = (uu + dd) / sqrt(2) T3 = (uu - dd) / sqrt(2) "Verify expectation values" check(dot(conj(T2),sigmaz,tauz,T2) == 1) check(dot(conj(T2),sigmax,taux,T2) == 1) check(dot(conj(T2),sigmay,tauy,T2) == -1) check(dot(conj(T3),sigmaz,tauz,T3) == 1) check(dot(conj(T3),sigmax,taux,T3) == -1) check(dot(conj(T3),sigmay,tauy,T3) == 1) "ok"
Run