Projective measurement

A projective measurement is specified by mutually orthogonal projections $P_i$ with ${\sum }_i{P}_i=I$. On a state $\rho$, outcome $i$ has probability $\mathrm{Tr}(P_i\rho )$.

Conditional on outcome $i$ of a projective measurement, the Lüders rule updates the state to

The post-measurement state is the conditional quantum state after a specified measurement outcome. For a projective measurement, it is given by the Lüders rule.

If the outcome of a projective measurement $\{P_i\}$ is discarded, its nonselective state update is the pinching channelIt removes coherence between distinct measurement subspaces.