Quantum Hilbert Transform

TL;DR

This paper introduces a quantum analogue of the classical Hilbert transform, enabling new quantum signal processing and secure information hiding techniques, with potential applications across various quantum technologies.

Contribution

It presents the first formulation of a quantum Hilbert transform and demonstrates its application in a quantum steganography protocol, bridging classical and quantum signal processing.

Findings

Quantum Hilbert transform formulated and defined.

Application demonstrated in quantum steganography.

Potential for advancements in quantum signal processing and secure communication.

Abstract

The Hilbert transform has been one of the foundational transforms in signal processing, finding it's way into multiple disciplines from cryptography to biomedical sciences. However, there does not exist any quantum analogue for the Hilbert transform. In this work, we introduce a formulation for the quantum Hilbert transform (QHT)and apply it to a quantum steganography protocol. By bridging classical phase-shift techniques with quantum operations, QHT opens new pathways in quantum signal processing, communications, sensing, and secure information hiding.