Superdense Coding in Resource Theory of Asymmetry
- URL: http://arxiv.org/abs/2002.01603v2
- Date: Thu, 14 Oct 2021 23:44:56 GMT
- Title: Superdense Coding in Resource Theory of Asymmetry
- Authors: Eyuri Wakakuwa
- Abstract summary: We consider a task in which classical information is encoded into a quantum system by an operation restricted by symmetry.
Our focus is on whether the capacity of an asymmetric state can be strictly larger than that of any symmetric states.
We prove that superdense coding is implementable if and only if the unitary representation of the symmetry is non-Abelian and reducible.
- Score: 9.137554315375919
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider a task in which classical information is encoded into a quantum
system by an operation restricted by symmetry. The maximum amount of classical
information that can be encoded under this restriction, namely the
symmetry-restricted classical information capacity, depends on the initial
state of the system. Our focus is on whether the capacity of an asymmetric
state can be strictly larger than that of any symmetric states, whereas the
latter is a strictly positive constant. That is, we ask whether an analog of
superdense coding is implementable in the resource theory of asymmetry. We
prove that superdense coding is implementable if and only if the unitary
representation of the symmetry is non-Abelian and reducible. Thereby we provide
an information theoretical classification of symmetries of quantum systems.
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