of two spin-half particles \(a\) and \(b\), using the same notation as in subsection 2.3. This is said to be an entangled state because it is not a product state of the form \(\ket{a,b} = \ket{a}\otimes\ket{b}\). It is easy to show that the corresponding projector \([\psi_0]\) does not commute with any projector on a nontrivial property of particle \(a\), such as \([z^+_a]\), or on a nontrivial property of \(b\). (The trivial properties are the identity and the zero projector.) Thus a quantum description that contains \([\psi_0]\) as a property cannot at the same time ascribe any nontrivial properties to either of the particles.