The basis states \left|a_{j}\right\rangle_{A} and \left|b_{j}\right\rangle_{B} may have completely different physical meanings; here we care only that the states of the decomposition can be la...The basis states \left|a_{j}\right\rangle_{A} and \left|b_{j}\right\rangle_{B} may have completely different physical meanings; here we care only that the states of the decomposition can be labelled with a single index, as opposed to two indices.
