Quantum Hilbert Transform

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.