Higher order nonclassicalities of finite dimensional coherent states: A comparative study

TL;DR

This paper compares the higher-order nonclassical properties of finite dimensional coherent states, revealing new insights into their quantum features using various nonclassicality witnesses and measures.

Contribution

It provides the first comparative analysis of higher-order nonclassicalities in finite dimensional coherent states using multiple witnesses and measures.

Findings

Higher order nonclassical properties are revealed for the first time.

Nonlinear and linear QCSs show distinct nonclassical features.

Higher order nonclassicality witnesses effectively detect complex quantum properties.

Abstract

Conventional coherent states (CSs) are defined in various ways. For example, CS is defined as an infinite Poissonian expansion in Fock states, as displaced vacuum state, or as an eigenket of annihilation operator. In the infinite dimensional Hilbert space, these definitions are equivalent. However, these definitions are not equivalent for the finite dimensional systems. In this work, we present a comparative description of the lower- and higher-order nonclassical properties of the finite dimensional CSs which are also referred to as qudit CSs (QCSs). For the comparison, nonclassical properties of two types of QCSs are used: (i) nonlinear QCS produced by applying a truncated displacement operator on the vacuum and (ii) linear QCS produced by the Poissonian expansion in Fock states of the CS truncated at (d-1)-photon Fock state. The comparison is performed using a set of nonclassicality witnesses (e.g., higher order antiubunching, higher order sub-Poissonian statistics, higher order squeezing, Agarwal-Tara parameter, Klyshko's criterion) and a set of quantitative measures of nonclassicality (e.g., negativity potential, concurrence potential and anticlassicality). The higher order nonclassicality witness have found to reveal the existence of higher order nonclassical properties of QCS for the first time.