Fock majorization in bosonic quantum channels with a passive environment
Résumé
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.
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