Lüders rule

Conditional on outcome

i

of a projective measurement, the Lüders rule updates the state to

ρ_{i} = \frac{P _{i} ρ P _{i}}{Tr ( P _{i} ρ )} .

Post-measurement state

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.

{P_{i}}

is discarded, its nonselective state update is the pinching channel

ρ ⟼ \sum_{i} P_{i} ρ P_{i} .

It removes coherence between distinct measurement subspaces.

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