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arXiv:2505.23581

Quantum Hilbert Transform

Nitin Jha, Abhishek Parakh

Published May 29, 2025• 0 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.2505.23581

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The main goal of steganography is to transmit hidden messages in legitimate-looking communication messages. Phase-domain information hiding, however, has not been fully explored for quantum systems. This work introduces a finite-dimensional Quantum Hilbert Transform (QHT) as a unitary phase operator based on the Quantum Fourier Transform. Using this construction, we develop a QHT-based quantum steganography scheme that embeds classical bits as weak signed phase perturbations of quantum cover states. Bob recovers the hidden message through binary state discrimination, block aggregation, and classical error-correcting decoding.
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In today’s era of escalating digital threats and the growing need for safeguarding sensitive information, this research strives to advance the field of information concealment by introducing a pioneering steganography methodology. Our approach goes beyond the conventional boundaries of image security by seamlessly integrating classical image processing techniques with the cutting-edge realm of quantum encoding. The foundation of our technique lies in the meticulous identification of distinctive features within the cover image, a crucial step achieved through the utilization of SIFT (Scale-Invariant Feature Transform). These identified key points are further organized into coherent clusters employing the K-means clustering algorithm, forming a structured basis for our covert communication process. The core innovation of this research resides in the transformation of the concealed message into a NEQR (Novel Enhanced Quantum Representation) code, a quantum encoding framework that leverages the power of quantum circuits. This transformative step ensures not only the secrecy but also the integrity of the hidden information, making it highly resistant to even the most sophisticated decryption attempts. The strategic placement of the quantum circuit representing the concealed message at the centroids of the clusters generated by the K-means algorithm conceals it within the cover image seamlessly. This fusion of classical image processing and quantum encoding results in an unprecedented level of security for the embedded information, rendering it virtually impervious to unauthorized access. Empirical findings from extensive experimentation affirm the robustness and efficacy of our proposed strategy.
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Several approaches and techniques exist to make communication via the internet secure, one of these approaches is steganography. Computer steganography can be defined as a method of hiding data in cover media so that others are not aware of its existence. Quantum computers, built on the principles of quantum physics, have introduced new possibilities for researchers in security and computer science. This paper explores the fundamentals of quantum computing, its achievements, and the challenges and future prospects it presents in the field of cryptography and steganography. Quantum computers give us a new approach to different kinds of complicated problems in security fields by creating multi-state computing spaces. The article deals with the steganography system which hides text inside images and after that realize quantum communication. The secret message is hidden in the cover image using Least Significant Bit (LSB) algorithm. The paper proposes an information transmission scheme with a quantum channel enabled. Quantum key distribution (QKD) is a secure communication method that implements a cryptographic protocol involving components of quantum mechanics.