 The state of the composite system assigns probabilities to outcomes of all experiments that can be performed on the composite system. We can also consider a restriction to experiments performed on system \(A\), or a restriction to experiments performed to \(B\).  Such restrictions yields states of \(A\) and \(B\), respectively, called the reduced states of the systems. When the state of the composite system \(AB\) is an entangled state, then the reduced states of \(A\) and \(B\) are mixed states. To see this, suppose that in the above state the vectors \(\ket{\phi_{1}}\) and \(\ket{\phi_{2}}\) represent distinguishable states. If one confines one’s attention to experiments performed on \(A\), it makes no difference whether an experiment is also performed on \(B\). An experiment performed on \(B\) that distinguishes \(\ket{\phi_{1}}\) and \(\ket{\phi_{2}}\) projects the state of \(A\) into either \(\ket{\psi_{1}}\) or \(\ket{\psi_{2}}\), with probabilities \(\abs{a}^{2}\) and \(\abs{b}^{2}\), respectively, and probabilities for outcomes of experiments performed on \(A\) are the corresponding averages of probabilities for states \(\ket{\psi_{1}}\) and \(\ket{\psi_{2}}\). These probabilities, as mentioned, are the same as those for the situation in which no experiment is performed on \(B\). Thus, even if no experiment is performed on \(B\), the probabilities of outcomes of experiments on \(A\) are exactly as if system \(A\) is either in the state represented by \(\ket{\psi_{1}}\) or the state represented by \(\ket{\psi_{2}}\), with probabilities \(\abs{a}^{2}\) and \(\abs{b}^{2}\), respectively.