Quantifying resources for Page-Wootters mechanism: Shared asymmetry as
relative entropy of entanglement
- URL: http://arxiv.org/abs/2007.15592v3
- Date: Mon, 2 Aug 2021 14:11:28 GMT
- Title: Quantifying resources for Page-Wootters mechanism: Shared asymmetry as
relative entropy of entanglement
- Authors: Rafael S. Carmo, Diogo O. Soares-Pinto
- Abstract summary: We explore the proposal based on resource theory of asymmetry, known as mutual or shared asymmetry.
We enunciation a theorem relating shared asymmetry of a bipartite state $rho_SR$ with the relative entropy of entanglement of textitinternal states.
We reinterpret the relation between Page-Wootters mechanism and entanglement and also open some paths to further studies.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Recently, some attention has been given to the so-called Page-Wootters
mechanism of quantum clocks. Among the various proposals to explore the
mechanism using more modern techniques, some have chosen to use a quantum
information perspective, defining and using informational measures to quantify
how well a quantum system can stand as a reference frame for other quantum
system. In this work, we explore the proposal based on resource theory of
asymmetry, known as mutual or shared asymmetry, which actually is equivalent to
the approach from coherence theory in the case of interest here: quantum
reference frames described by the $U(1)$ compact group. We extend some previous
results in literature about shared asymmetry and Page-Wootters mechanism to
more general cases, culminating in the enunciation of a theorem relating shared
asymmetry of a bipartite state $\rho_{SR}$ with the relative entropy of
entanglement of \textit{internal states} $\rho_M$ on the charge sectors of the
Hilbert space $\mathcal{H}_S\otimes\mathcal{H}_R$. Using this result we
reinterpret the relation between Page-Wootters mechanism and entanglement and
also open some paths to further studies.
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