Axiomatic Approach to Quantum Superchannels

TL;DR

This paper develops an axiomatic framework for quantum superchannels focusing on their action on the operator system spanned by quantum channels, leading to more precise characterizations and insights into their structure.

Contribution

It introduces a new axiomatic approach to quantum superchannels on a smaller domain, revealing non-uniqueness and implications for auxiliary dimensions and tensor products.

Findings

Extended the characterization of superchannels to a smaller operator system.

Discovered non-uniqueness in superchannel extensions.

Analyzed effects on auxiliary dimensions and tensor products.

Abstract

Quantum superchannels are maps whose input and output are quantum channels. Rather than taking the domain to be the space of all linear maps we motivate and define superchannels on the operator system spanned by quantum channels. Extension theorems for completely positive maps allow us to apply the characterisation theorem for superchannels to this smaller set of maps. These extensions are non unique, showing two different superchannels act the same on all input quantum channels, and so this new definition on the smaller domain captures more precisely the action of superchannels as transformations between quantum channels. The non uniqueness can affect the auxilliary dimension needed for the characterisation as well as the tensor product of the superchannels.