Subsystems as subsets of quantum channels, graded subalgebras, and the strange case of blind agents

Operational definitions identify subsystems through the transformations an agent can perform. This talk classifies complementary, bicommutant-closed subsystems using unitary channels, whose disregard for global phase permits possibilities beyond conventional operator subalgebras. The classification involves graded subalgebras. Some resulting subsystems are nontrivial yet support no measurements, raising a foundational choice between excluding them and accepting agents that act without being able to observe.