  For example, the state of the L-particle having z-spin ‘up’ (i.e., spinning ‘up’ about the z-axis) can be represented by the vector |z-up&gt; in the Hilbert space associated with the L-particle, and the state of the L-particle having z-spin ‘down’ (i.e., spinning ‘down’ about the z-axis) can be represented by the orthogonal vector, |z-down&gt;. Particle pairs may be in a state in which the L-particle and the R-particle have opposite spins, for instance either a state |ψ1&gt; in which the L-particle has z-spin ‘up’ and the R-particle has z-spin ‘down,’ or a state |ψ2&gt; in which the L-particle has z-spin ‘down’ and the R-particle has z-spin ‘up.’ Each of these states is represented by a tensor product of vectors in the Hilbert space of the particle pair:  |ψ1&gt;  = |z-up&gt;L |z-down&gt;R and |ψ2&gt; = |z-down&gt;L |z-up&gt;R; where the subscripts L and R refer to the Hilbert spaces associated with the L- and the R-particle, respectively. But particle pairs may also be in a superposition of these states, i.e., a state that is a linear sum of the states |ψ1&gt; and |ψ2&gt;, e.g. the state represented by