Induced entanglement entropy of harmonic oscillators in noncommutative phase space

Abstract

We study the entanglement entropy of harmonic oscillators in noncommutative phase space. We propose a new definition of quantum Rényi entropy based on Wigner functions in noncommutative phase space. 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 noncommutative parameters, the harmonic oscillators can be entangled in noncommutative phase space. This is a new entanglement-like effect caused by the noncommutativity of the phase space.

References in corpus (31)

• Quantum entanglement
• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum entanglement in condensed matter systems
• Space-Time Noncommutative Field Theories And Unitarity
• Quantum mechanics on the noncommutative plane and sphere
• The exotic Galilei group and the "Peierls substitution"
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• Fractional Angular Momentum in Noncommutative Space
• Entropy and Wigner Functions
• Deformation quantization in the teaching of quantum mechanics
• A Novel Approach to Noncommutativity in Planar Quantum Mechanics
• Representation of noncommutative phase space
• Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory
• Holographic complexity and non-commutative gauge theory
• Bianchi spacetimes in noncommutative phase-space
• Entanglement due to noncommutativity in the phase-space
• Nonclassicality versus entanglement in a noncommutative space
• Inertial spin Hall effect in noncommutative space
• Massive Neutrino in Non-commutative Space-time
• Large scale quantum entanglement in de Sitter spacetime
• Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space
• A Classical Bound on Quantum Entropy
• A new kind of representations on noncommutative phase space
• Quantum entanglement in a non-commutative system
• Entropy and Information of a harmonic oscillator in a time-varying electric field in 2D and 3D noncommutative spaces
• Reality in Noncommutative Gravity
• Time dependence of entanglement entropy on the fuzzy sphere
• Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
• Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
• Entanglement entropy on a fuzzy sphere with a UV cutoff

Cited by in corpus (5)

• On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field
• Connes spectral distance and nonlocality of generalized noncommutative phase spaces
• Tuning the separability in noncommutative space
• Deformation quantization for systems with second-class constraints in deformed fermionic phase space
• Connes distance of $2D$ harmonic oscillators in quantum phase space