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A finite family of quantum states is antidistinguishable if a quantum measurement has labelled outcomes such that each outcome has zero probability for its corresponding state, while the outcomes form a complete quantum measurement. It can exclude a state without identifying which state was prepared. The PBR exclusion measurement for zero and plus supplies a four-state projective measurement example.

In the ABL rule, probabilities depend on the full intermediate quantum measurement instrument. A binary Lüders rule quantum measurement preserves coherence within its unresolved complement, whereas a fully resolved projective measurement removes it. Summing fine-grained probabilities after quantum measurement does not generally reproduce the coarse-grained experiment. Different postselection success rates are part of the distinction.

Logical measurement depth is the number of sequential measurement layers required by outcome-dependent basis choices. Depth one means all bases are fixed in advance, so the quantum measurements on distinct qubits can be simultaneous. Classical output corrections may still depend on all outcomes. This does not assert depth-one graph-state preparation or constant-depth classical processing.

Measurement-based quantum computation prepares an entangled resource quantum state, then applies single-qubit quantum measurements, potentially adapting later bases to earlier outcomes. Pauli frame tracking and classical outcome processing convert random physical branches into a specified logical computation. Graph states and one-bit teleportation provide a concrete construction.

A measurement interaction correlates a measured system's alternatives with distinguishable states of an apparatus. Reading the apparatus then implements the associated quantum measurement.

For a uniform prestate in $N+1$ dimensions and poststate proportional to ${\sum }_{i=1}^N|i⟩-(N-1)|N+1⟩$, each binary question $P_i$ versus $I-P_i$ has conditional probability one for $i\le N$. A fully resolved quantum measurement instead assigns $1/D$ to each of the first $N$ outcomes and $(N-1{)}^2/D$ to the last. The context dependence of pre- and post-selected measurements explains why these alternative certainties do not imply simultaneous properties.

An ontological model associates each quantum state preparation with a probability distribution over underlying physical states $\lambda$. A quantum measurement's response probabilities depend on its specification and $\lambda$, sum to one, and reproduce the Born rule when averaged over the preparation distribution. The model need not assign deterministic outcomes. Overlap or disjointness of preparation measures defines the psi-epistemic model versus psi-ontic model distinction.