Canonical Typicality under General Quantum Channels

With the control of increasingly complex quantum systems, the relevant degrees of freedom we are interested in may not be those traditionally addressed by statistical quantum mechanics. Here, we employ quantum channels to define generalized subsystems, capturing the pertinent degrees of freedom, and obtain their associated canonical state. We show that the generalized subsystem description from almost any microscopic pure state of the whole system will behave similarly to its corresponding canonical state. Such canonical typicality behavior depends on the entropy of the channel used to define the generalized subsystem.