Fock majorization in bosonic quantum channels with a passive environment

TL;DR

This paper introduces passive-environment bosonic channels, showing they preserve Fock majorization, which links disorder and energy, thus advancing understanding of quantum thermodynamics and energy-preserving quantum operations.

Contribution

It defines a new class of energy-preserving quantum channels and proves they preserve Fock majorization, extending to passive states and active Gaussian unitaries, with implications for quantum thermodynamics.

Findings

Passive-environment bosonic channels preserve Fock majorization.

Preservation extends to regular majorization over passive states.

The class generalizes thermal operations and informs quantum thermodynamics.

Abstract

We introduce a class of quantum channels called passive-environment bosonic channels. These channels are relevant from a quantum thermodynamical viewpoint because they correspond to the energy-preserving linear coupling of a bosonic system with a bosonic environment that is in a passive state (no energy can be extracted from it by using a unitary transformation) followed by discarding the environment. The Fock-majorization relation defined in [New J. Phys. 18, 073047 (2016)] happens to be especially useful in this context as, unlike regular majorization, it connects the disorder of a state together with its energy. Our main result here is the preservation of Fock majorization across all passive-environment bosonic channels. This implies a similar preservation property for regular majorization over the set of passive states, and it also extends to passive-environment channels whose Stinespring dilation involves an active Gaussian unitary. Beyond bosonic systems, the introduced class of passive environment operations naturally generalizes thermal operations and is expected to provide new insights into the thermodynamics of quantum systems.