Lossless Quantum Data Compression and Secure Direct Communication- New concepts and methods for quantum information theory

Jincheng Zhang

This paper explores the application of Quantum Монхоуф Transform (QMT) for image processing, specifically focusing on lossless compression and manipulation. Traditional image processing techniques often introduce information loss, leading to degradation in image quality. We propose utilizing the QMT, a quantum mechanical analogue of the Монхоуф Transform, to achieve lossless image processing. The core concept involves encoding image data into the basis vectors of the QMT and subsequently leveraging the QMT's inherent properties for image transformation. This approach draws upon both quantum information theory and the principles of the Монхоуф Transform, offering a novel pathway for efficient and lossless image handling. The theoretical framework and potential advantages of this method are presented, outlining a promising direction for future research in quantum image processing. The key mathematical framework is built upon the concept of quantum superposition and measurement, central to the QMT. The primary goal is to demonstrate a method for lossless image manipulation without the inherent distortions of conventional approaches.

Seema Ukidve, Ramsagar Yadav, Mukhdeep Singh Manshahia +1 more

Kim Joris Boström, Timo Felbinger

In order to compress quantum messages without loss of information it is necessary to allow the length of the encoded messages to vary. We develop a general framework for variable-length quantum messages in close analogy to the classical case and show that lossless compression is only possible if the message to be compressed is known to the sender. The lossless compression of an ensemble of messages is bounded from below by its von-Neumann entropy. We show that it is possible to reduce the number of qbits passing through a quantum channel even below the von Neumann entropy by adding a classical side channel. We give an explicit communication protocol that realizes lossless and instantaneous quantum data compression and apply it to a simple example. This protocol can be used for both online quantum communication and storage of quantum data.

David S. Simon

Wim van Dam, Simone Severini B, Viv M. Kendon

Kim Joris Boström

Based on the concept of many-letter theory a general characterization of quantum codes using the Kraus representation is given. Compression codes are defined by their property of decreasing the average information content of a given a priori message ensemble. Lossless quantum codes, in contrast to lossy codes, provide the retrieval of the original input states with perfect fidelity. A general lossless coding scheme is given that translates between two quantum alphabets. It is shown that this scheme is never compressive. Furthermore, a lossless quantum coding scheme, analog to the classical Huffman scheme but different from the Braunstein scheme, is implemented, which provides optimal compression. Motivated by the concept of lossless quantum compression, an observable is defined that measures the amount of compressible quantum information contained in a particular message with respect to a given \\emph{a priori} message ensemble. The average of this observable yields the von Neumann entropy, which is finally established as the amount of compressible quantum information of any message ensemble, confirming its commonly assigned meaning.