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}
}
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… 
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References

SHOWING 1-10 OF 65 REFERENCES
On quantum Rényi entropies: A new generalization and some properties
TLDR
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
TLDR
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
TLDR
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
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
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
TLDR
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.
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
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
TLDR
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.
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