I'm still quite confused about the post-measurement state when a node of a cluster state is measured.

As far as I'm aware, for a cluster state, a given node $j$ will have a stabilizer

$$X_j\bigotimes_{k\in N_j}Z_k$$

for the set of nodes $N_j$ around $j$.

I don't understand the post-measurement state of one of these nodes. Say this $j$-th node is measured, the node will disappear from the cluster, but what will the remaining cluster state look like and what will the stabilizers be for each remaining node?

An explanation or a link to an explanation would be wonderful.

  • $\begingroup$ Are you asking about measurement in a specific basis? $\endgroup$
    – DaftWullie
    Jun 7 at 6:19

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