= Relative state of a bipartite vector
{title2=$|\eta_j\rangle=(\langle j|\otimes I)|v\rangle$}
= Relative state
{synonym}
For a bipartite vector $|v\rangle\in\mathcal H_R\otimes\mathcal H_A$ and a chosen orthonormal basis of $R$, the generally unnormalized relative state on $A$ is obtained by the partial inner product with one basis vector. It gives the expansion $|v\rangle=\sum_j|j\rangle\otimes|\eta_j\rangle$. The squared norm of a relative state is the probability of its corresponding basis outcome when $|v\rangle$ is normalized. Relative states of eigenvectors of a <Choi matrix> construct the columns of its <Kraus operators>.
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