diff --git a/lib_q_computer_math.py b/lib_q_computer_math.py
index 67a565e..16b2847 100644
--- a/lib_q_computer_math.py
+++ b/lib_q_computer_math.py
@@ -174,13 +174,13 @@ class State(Vector):
         return theta, phi
 
     def rotate_x(self, theta):
-        return self | Rx(theta)
+        return Rx(theta).on(self)
 
     def rotate_y(self, theta):
-        return self | Ry(theta)
+        return Ry(theta).on(self)
 
     def rotate_z(self, theta):
-        return self | Rz(theta)
+        return Rz(theta).on(self)
 
     def __repr__(self):
         if not self.name:
@@ -529,34 +529,34 @@ Z = UnitaryOperator([[1, 0],
                     name="Z")
 
 
-# TODO: These are not the rotations that are specified commonly e.g. in
+# TODO: These are rotations that are specified commonly e.g. in
 #       https://www.quantum-inspire.com/kbase/rotation-operators/
 #       http://www.vcpc.univie.ac.at/~ian/hotlist/qc/talks/bloch-sphere-rotations.pdf
-#       and elsewhere.
-#       --------------
-#       Multiply the bellow ones by the following to get the commonly given
-#       X = [[1, -1j][-1j, 1]]
-#       Y = [[1, -1j][-1j, 1]]
-#       Z = [[1j, 0][1j, 0]]
+#       and elsewhere DO NOT equate X, Y and Z for theta=np.pi
+#       ??????????????????????????????????????????????????????
 
 def Rx(theta):
-    return UnitaryOperator([[np.cos(theta / 2), np.sin(theta / 2)],
-                            [np.sin(theta / 2), np.cos(theta / 2)]],
+    return UnitaryOperator([[np.cos(theta / 2), -1j * np.sin(theta / 2)],
+                            [-1j * np.sin(theta / 2), np.cos(theta / 2)]],
                            name="Rx")
 
 
 def Ry(theta):
-    return UnitaryOperator([[np.cos(theta / 2), -1j * np.sin(theta / 2)],
-                            [1j * np.sin(theta / 2), np.cos(theta / 2)]],
+    return UnitaryOperator([[np.cos(theta / 2), -np.sin(theta / 2)],
+                            [np.sin(theta / 2), np.cos(theta / 2)]],
                            name="Ry")
 
 
 def Rz(theta):
-    return UnitaryOperator([[1j * np.power(np.e, -1j * theta / 2), 0],
-                            [0, 1j * np.power(np.e, 1j * theta / 2)]],
+    return UnitaryOperator([[np.power(np.e, -1j * theta / 2), 0],
+                            [0, np.power(np.e, 1j * theta / 2)]],
                            name="Rz")
 
 
+# def unitary(alpha, vector:Vector, theta):
+#     return np.exp(1j * alpha)
+
+
 H = UnitaryOperator([[1 / np.sqrt(2), 1 / np.sqrt(2)],
                      [1 / np.sqrt(2), -1 / np.sqrt(2)], ],
                     name="H")
@@ -628,10 +628,19 @@ def test_unitary_hermitian():
     assert_raises(TypeError, "Not a Unitary matrix", UnitaryMatrix, not_u_not_h)
 
 
+def abs_squared(x):
+    return np.abs(x) ** 2
+
+
 def testRotPauli():
-    assert Rx(np.pi) == X
-    assert Ry(np.pi) == Y
-    assert Rz(np.pi) == Z
+    # From http://www.vcpc.univie.ac.at/~ian/hotlist/qc/talks/bloch-sphere.pdf
+    # / slide 11:
+    # However, the only measurable quantities are the probabilities
+    # |α|**2 and |β|**2, so multiplying the state by an arbitrary factor
+    # exp(iγ) (a global phase) has no observable consequences
+    assert np.allclose(abs_squared(Rx(np.pi).m), abs_squared(X.m))
+    assert np.allclose(abs_squared(Ry(np.pi).m), abs_squared(Y.m))
+    assert np.allclose(abs_squared(Rz(np.pi).m), abs_squared(Z.m))
 
 
 def test():
@@ -1007,6 +1016,6 @@ def test_quantum_processor():
 
 if __name__ == "__main__":
     test()
-    pp(_p.get_bloch_coordinates())
+    # pp(_p.get_bloch_coordinates())
     # test_to_from_angles()
     # test_quantum_processor()
diff --git a/papers/bloch-sphere.pdf b/papers/bloch-sphere.pdf
new file mode 100644
index 0000000..aa5e710
Binary files /dev/null and b/papers/bloch-sphere.pdf differ