Some properties of coherent states with singular complex matrix argument

TL;DR

This paper introduces a new class of coherent states with singular matrix arguments, demonstrating their properties and connections to qubits and entropy, expanding the theoretical framework of quantum states.

Contribution

It presents a novel form of coherent states involving singular matrix arguments and explores their fundamental properties and applications.

Findings

Coherent states satisfy all standard conditions for pure and mixed states.

Established links between these states and qubit representations.

Analyzed von Neumann entropy in the context of the new states.

Abstract

In the paper our aim was to study the properties of a new version of coherent states whose argument is a linear combination of two special singular square 2 x 2 matrix, having a single nonzero element, equal to 1, and two labeling complex variables as developing coefficients. We have shown that this new version of coherent states satisfies all the conditions imposed on coherent states, both of pure, as well as the mixed (thermal) states characterized by the density operator. As applications, we examined the connection between these coherent states and the notions of qubits and von Neuman entropy.