# Rényi and von Neumann entropies of thermal state in Generalized Uncertainty Principle-corrected harmonic oscillator

@article{Kim2021RnyiAV,
title={R{\'e}nyi and von Neumann entropies of thermal state in Generalized Uncertainty Principle-corrected harmonic oscillator},
author={Mu-Seong Kim and Mi-Ra Hwang and Eylee Jung and Daekil Park},
journal={Modern Physics Letters A},
year={2021}
}
• Published 4 June 2020
• Computer Science
• Modern Physics Letters A
The Rényi and von Neumann entropies of thermal state in generalized uncertainty principle (GUP)-corrected single harmonic oscillator system are explicitly computed within the first order of GUP parameter [Formula: see text]. While the von Neumann entropy with [Formula: see text] exhibits a monotonically increasing behavior in external temperature, the nonzero GUP parameter makes a decreasing behavior at large temperature region. As a result, for the case of [Formula: see text], the von Neumann…
2 Citations

## Figures and Tables from this paper

Dispersion and entropy-like measures of multidimensional harmonic systems: application to Rydberg states and high-dimensional oscillators
• Physics
• 2020
The spreading properties of the stationary states of the quantum multidimensional harmonic oscillator are analytically discussed by means of the main dispersion measures (radial expectation values)

## References

SHOWING 1-10 OF 65 REFERENCES
On quantum Rényi entropies: A new generalization and some properties
• Computer Science
• 2013
This work proposes a new quantum generalization of the family of Renyi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropies as special cases, thus encompassing most quantum entropie in use today.
Thermal entanglement phase transition in coupled harmonic oscillators with arbitrary time-dependent frequencies
This work derives explicitly the thermal state of the two-coupled harmonic oscillator system when the spring and coupling constants are arbitrarily time-dependent and can protect the entanglement against the external temperature by introducing large difference of initial and final frequencies.
Smooth Entropies and the Quantum Information Spectrum
• Computer Science
IEEE Transactions on Information Theory
• 2009
The spectral entropy rate can be seen as the asymptotic limit of the smooth entropy, which applies to the quantum setting and thus includes the classical setting as a special case.
Scaling of the Rényi entropies in gapped quantum spin systems: Entanglement-driven order beyond symmetry breaking
• Physics
• 2012
We investigate the scaling of the R\'enyi $\alpha$-entropies in one-dimensional gapped quantum spin models. We show that the block entropies with $\alpha > 2$ violate the area law monotonicity and
Renyi entropy of the XY spin chain
• Physics
• 2008
We consider the one-dimensional XY quantum spin chain in a transverse magnetic field. We are interested in the Renyi entropy of a block of L neighboring spins at zero temperature on an infinite
On the Quantum Rényi Relative Entropies and Related Capacity Formulas
• Computer Science
IEEE Transactions on Information Theory
• 2011
It is shown that various generalizations of the Holevo capacity, defined in terms of the α-relative entropies, coincide for the parameter range α ∈ (0,2], and an upper bound on the one-shot ε-capacity of a classical-quantum channel interms of these capacities is given.
Measuring Gaussian quantum information and correlations using the Rényi entropy of order 2.
• Computer Science, Physics
Physical review letters
• 2012
We demonstrate that the Rényi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon
Path integral for nonrelativistic generalized uncertainty principle corrected Hamiltonian
• Physics
• 2012
The generalized uncertainty principle (GUP) has brought the idea of the existence of a minimum measurable length in quantum physics. Depending on this GUP, the nonrelativistic Hamiltonian at the
Classical information capacity of a class of quantum channels
• Computer Science
• 2005
The additivity of the minimal output Renyi entropies with entropic parameters α ∊ [0, 2], generalizing an argument by Alicki and Fannes, is proved and a weak form of covariance is introduced of a channel to relate these results to the classical information capacity.