Induced entanglement entropy of harmonic oscillators in non-commutative phase space

@article{Lin2018InducedEE,
  title={Induced entanglement entropy of harmonic oscillators in non-commutative phase space},
  author={Bingsheng Lin and Jian Xu and Tai-Hua Heng},
  journal={Modern Physics Letters A},
  year={2018}
}
We study the entanglement entropy of harmonic oscillators in non-commutative phase space (NCPS). We propose a new definition of quantum Rényi entropy based on Wigner functions in NCPS. Using the Rényi entropy, we calculate the entanglement entropy of the ground state of the 2D isotropic harmonic oscillators. We find that for some values of the non-commutative parameters, the harmonic oscillators can be entangled in NCPS. This is a new entanglement-like effect caused by the non-commutativity of… 

Figures from this paper

Entanglement induced by noncommutativity: anisotropic harmonic oscillator in noncommutative space

Quantum entanglement, induced by spatial noncommutativity, is investigated for an anisotropic harmonic oscillator. Exact solutions for the system are obtained after the model is re-expressed in terms

Connes distance of 2D harmonic oscillators in quantum phase space

We study the Connes distance of quantum states of $2D$ harmonic oscillators in phase space. Using the Hilbert-Schmidt operatorial formulation, we construct a boson Fock space and a quantum Hilbert

Entanglement in phase-space distribution for an anisotropic harmonic oscillator in noncommutative space

  • P. Patra
  • Physics
    Quantum Inf. Process.
  • 2023
The bi-partite Gaussian state, corresponding to an anisotropic harmonic oscillator in a noncommutative space (NCS), is investigated with the help of Simon’s separability condition (generalized

On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field

A Charged harmonic oscillator in a magnetic field, Landau problems, and an oscillator in a noncommutative space, share the same mathematical structure in their Hamiltonians. We have considered a

Connes spectral distance and nonlocality of generalized noncommutative phase spaces

We study the Connes spectral distance of quantum states and analyse the nonlocality of a 4D generalized noncommutative phase space. By virtue of the Hilbert–Schmidt operatorial formulation, we obtain

References

SHOWING 1-10 OF 50 REFERENCES

Quantum entanglement in a noncommutative system

We explore the effect of two-dimensional position-space noncommutativity on the bipartite entanglement of continuous-variable systems. We first extend the standard symplectic framework for studying

Energy Spectra of the Harmonic Oscillator in a Generalized Noncommutative Phase Space of Arbitrary Dimension

We use the invariant eigen-operator method to study the higher-dimensional harmonic oscillator in a type of generalized noncommutative phase space, and obtain the explicit expression of the energy

Entanglement due to noncommutativity in phase space

The entanglement criterion for continuous variable systems and the conditions under which the uncertainty relations are fulfilled are generalized to the case of a noncommutative phase space. The

Time dependence of entanglement entropy on the fuzzy sphere

A bstractWe numerically study the behaviour of entanglement entropy for a free scalar field on the noncommutative (“fuzzy”) sphere after a mass quench. It is known that the entanglement entropy

Tsallis entropy in phase-space quantum mechanics

In this paper we define the quantum version of the Tsallis entropy in terms of quantum phase space distribution functions. The quantum Tsallis entropy is compared with Kenfack's nonclassicality

DEFORMATION QUANTIZATION FOR COUPLED HARMONIC OSCILLATORS ON A GENERAL NONCOMMUTATIVE SPACE

Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily

Entropy and wigner functions

  • ManfrediFeix
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 2000
It is shown that smoothing of the Wigner function induces an increase in entropy, and this fact is used to derive some simple rules to construct positive-definite probability distributions which are also admissible Wigninger functions.

Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space

We consider rotationally invariant noncommutative algebra with tensors of noncommutativity constructed with the help of additional coordinates and momenta. The algebra is equivalent to the well-known

Large scale quantum entanglement in de Sitter spacetime

We investigate quantum entanglement between two symmetric spatial regions in de Sitter space with the Bunch-Davies vacuum. As a discretized model of the scalar field for numerical simulation, we