Extended Weyl-Heisenberg algebra, phase operator, unitary depolarizers and generalized Bell states

TL;DR

This paper explores finite-dimensional representations of extended Weyl-Heisenberg algebra, introduces a unitary phase operator and its eigenstates, constructs unitary depolarizers, and generates generalized Bell states using phase operators and mutually unbiased bases.

Contribution

It provides a novel framework connecting Weyl-Heisenberg algebra, phase operators, depolarizers, and Bell states in finite dimensions.

Findings

Construction of unitary phase operators and eigenstates.

Method to generate generalized Bell states.

Expression of Bell states via mutually unbiased bases.

Abstract

Finite dimensional representations of extended Weyl-Heisenberg algebra are studied both from mathematical and applied viewpoints. They are used to define unitary phase operator and the corresponding eigenstates (phase states). It is also shown that the unitary depolarizers can be constructed in a general setting in terms of phase operators. Generation of generalized Bell states using the phase operator is presented and their expressions in terms of the elements of mutually unbiased bases are given.