Quantum theory of channeling

V.A. Khodyrev

Jae Hyeok Shin

In quantum information theory, there are few quantum channels whose specific formulas and properties are known.In this thesis, we introduce EPOSIC channels, a class of SU(2)-irreducibly covariant quantum channels, and compute their χ-capacity and entropy in some cases.We review the basics of group representation theory and quantum information theory, and we construct EPOSIC channels, a new class of quantum channels, using representation theory.We also study specific formulas and properties of EPOSIC channels.

Javid Naikoo, Subhashish Banerjee, R. Srikanth

Yunchao Liu, Xiao Yuan

In this work, the authors propose a general resource framework for quantum channels, based on which they study general connections between channel and state resource theories and investigate general properties of the operational resource theory of channels, without specifying the resource being studied. Concrete examples in the resource theory of coherence are also provided.

Hidetosi Takahasi

Ryuji Takagi, Kun Wang, Masahito Hayashi

We introduce a resource theory of channels relevant to communication via quantum channels, in which the set of constant channels-useless channels for communication tasks-are considered as free resources. We find that our theory with such a simple structure is useful to address central problems in quantum Shannon theory-in particular, we provide a converse bound for the one-shot nonsignaling assisted classical capacity that naturally leads to its strong converse property, as well as obtain the one-shot channel simulation cost with nonsignaling assistance. We clarify an intimate connection between the nonsignaling assistance and our formalism by identifying the nonsignaling assisted channel coding with the channel transformation under the maximal set of resource nongenerating superchannels, providing a physical characterization of the latter. Our results provide new perspectives and concise arguments to those problems, connecting the recently developed fields of resource theories to "classic" settings in quantum information theory and shedding light on the validity of resource theories of channels as effective tools to address practical problems.