Generalized $\alpha$-Observational Entropy
- URL: http://arxiv.org/abs/2312.03572v1
- Date: Wed, 6 Dec 2023 16:04:52 GMT
- Title: Generalized $\alpha$-Observational Entropy
- Authors: Shivam Sinha and S. Aravinda
- Abstract summary: We extend the scope of observational entropy by generalizing it to a parameterized version called $alpha$-Observational entropy ($alpha$-OE)
$alpha$-OE is expressed in terms of the Petz-R'enyi relative entropy between the states on which a quantum-to-classical channel is applied.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Recognizing the inadequacy of existing measures for thermodynamic entropy,
recent research focuses on observational Eetropy (OE) as a promising
alternative, offering practical applicability and theoretical insights. In this
work, we extend the scope of observational entropy by generalizing it to a
parameterized version called $\alpha$-Observational entropy ($\alpha$-OE).
$\alpha$-OE is expressed in terms of the Petz-R\'{e}nyi relative entropy
between the states on which a quantum-to-classical channel is applied. It is
also expressed by using Sandwitched relative entropy. We prove various
properties of the $\alpha$-OE, which are the generalization of the properties
of OE, including the monotonically increasing of $\alpha$-OE as a function of
refinement of coarse-graining. The generalized quantum relative entropies play
a central role in many areas of quantum information theory, and we provide a
connection of these entropic quantities to thermodynamic properties.
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