Definition: One-shot realization model

A one-shot realization consists of:

1. a pure initialized environment;

2. an isometry from the input into output tensored with environment;

3. a projective environment readout whose orthogonal blocks are labelled by $x$;

4. optional classical coarse-graining of a fully read fine index.

Arbitrary coherent unitaries are available. A classical outcome register, if explicitly retained quantumly, is counted separately; it is not a free output qubit.