Canonical typicality under general quantum channels

TL;DR

This paper extends the concept of canonical typicality to generalized quantum subsystems defined via quantum channels, showing that typicality emerges under broad conditions related to the channel's entropy.

Contribution

It introduces a framework for defining generalized subsystems using quantum channels and demonstrates that canonical typicality persists in this generalized setting, depending on the channel's entropy.

Findings

Canonical typicality holds for generalized subsystems defined by quantum channels.

The emergence of typicality depends on the entropy of the channel used.

Almost any pure state of the whole system leads to a similar generalized canonical state.

Abstract

With the control of ever more complex quantum systems becoming a reality, new scenarios are emerging where generalizations of the most foundational aspects of statistical quantum mechanics are imperative. In such experimental scenarios the often natural correspondence between the particles that compose the system and the relevant degrees-of-freedom might not be observed. In the present work we employ quantum channels to define generalized subsystems, which should capture the pertinent degrees-of-freedom, and obtain their associated canonical state. Moreover, we show that generalized subsystems also display the phenomena of canonical typicality, i.e., the generalized subsystem description generated from almost any microscopic pure state of the whole system will behave similarly as the corresponding canonical state. In particular we demonstrate that the property regulating the emergence of the canonical typicality behavior is the entropy of the channel used to define the generalized subsystem.