Quadrature Uncertainty and Information Entropy of Quantum Elliptical Vortex States

TL;DR

This paper investigates the quantum elliptical vortex states' quadrature uncertainty and entropy, revealing how vorticity and ellipticity influence entanglement and information capacity, with implications for quantum information processing.

Contribution

It provides a detailed analysis of quadrature uncertainty and entropy in quantum elliptical vortex states, highlighting the effects of vorticity and ellipticity on entanglement and information bounds.

Findings

Entropy increases with vorticity for both modes.

Maximum entanglement occurs at an optimal ellipticity.

Entropic inequalities are satisfied only within specific ellipticity ranges.

Abstract

We study the quadrature uncertainty of the quantum elliptical vortex state using the associated Wigner function. Deviations from the minimum uncertainty states were observed due to the absence of the Gaussian nature. In our study of the entropy, we noticed that with increasing vorticity, entropy increases for both the modes. We further observed that, there exists an optimum value of ellipticity which gives rise to maximum entanglement of the two modes of the quantum elliptical vortex states. A further increase in ellipticity reduces the entropy thereby resulting in a loss of information carrying capacity. We check the validity of the entropic inequality relations, namely the subaddivity and the Araki-Lieb inequality. The later was satisfied only for a very small range of the ellipticity of the vortex while the former seemed to be valid at all values.