Quadrature uncertainty and information entropy of quantum elliptical vortex states

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.

Entanglement measure using Wigner function: Case of generalized vortex state formed by multiphoton subtraction

“…We highlight the negativity of the Winger function, which depicts non classicality [15], as a measure of entanglement. For our study, we consider optical vortex states formed by quantized radiation fields [16][17][18][19][20][21]. These are easy to generate non-Gaussian states of light.…”

Generating a perfect quantum optical vortex

“…A vortex state of topological index l carries with it an orbital angular momentum l . It has also been reported that higher the order, higher is the entanglement [14]. Although l can range from 0 to ∞, neglecting the handedness, in practice, it is observed, higher the order, larger is the spread of the vortex core.…”

“…In general, photon pairs produced in SPDC output belong to the larger class of Gaussian states and has been subjected to detailed study and scrutiny over the years in the context of quantum information [9]. Lately though, there has been increasing focus on a new class of states being generated from SPDC photons called the quantum vortex states [10][11][12][13][14][15][16]. These are non-Gaussian quantum states exhibiting phase singularity or topological defect.…”

Entanglement propagation of a quantum optical vortex state

“…Any other ratio of mixing gives rise to an elliptical vortex which is far more general. It has also been pointed out that elliptical vortex states have higher entropy and hence higher information carrying capability [17]. The generalized vortex state can be written as…”

“…Entanglement being a fundamental resource in quantum information processing, it is interesting to study states with enhanced entanglement from a task oriented point of view. It has been shown that vortex states carry more entanglement compared to the Gaussian states from which they are generated and the entanglement carried can be controlled by altering the squeezing parameter or the ratio of mixing of the two input modes in a beam splitter [17].…”