Fractional Hadamard transform with continuous variables in the context of quantum optics

TL;DR

This paper introduces a quantum fractional Hadamard transform for continuous variables in quantum optics, demonstrating its decomposition and extension to entangled states, offering enhanced flexibility for signal representation.

Contribution

It presents the first quantum fractional Hadamard transform with continuous variables, including its decomposition and extension to bipartite entangled states.

Findings

Decomposition into single-mode fractional and squeezing operators

Extension to bipartite entangled states

Enhanced signal representation flexibility

Abstract

We introduce the quantum fractional Hadamard transform with continuous variables. It is found that the corresponding quantum fractional Hadamard operator can be decomposed into a single-mode fractional operator and two single-mode squeezing operators. This is extended to the entangled case by using the bipartite entangled state representation. The new transformation presents more flexibility to represent signals in the fractional Hadamard domain with extra freedom provided by an angle and two-squeezing parameters.