Related papers: Data Compression for Quantum Code
The quantum entropy-typical subspace theory is specified. It is shown that any mixed state with von Neumann entropy less than h can be preserved approximately by the entropy-typical subspace with entropy= h. This result implies an universal…
We design a quantum method for classical information compression that exploits the hidden subgroup quantum algorithm. We consider sequence data in a database with a priori unknown symmetries of the hidden subgroup type. We prove that data…
When classical or quantum information is broadcast to separate receivers, there exist codes that encrypt the encoded data such that the receivers cannot recover it when performing local operations and classical communication, but they can…
Quantum information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control on the way quantum dynamics unfolds in the information-processing system. In…
We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert space dimension…
Huffman Compression, also known as Huffman Coding, is one of many compression techniques in use today. The two important features of Huffman coding are instantaneousness that is the codes can be interpreted as soon as they are received and…
Coded source compression, also known as source compression with helpers, has been a major variant of distributed source compression, but has hitherto received little attention in the quantum regime. This work treats and solves the…
Based on the concept of many-letter theory, an observable is defined measuring the raw quantum information content of single messages. A general characterization of quantum codes using the Kraus representation is given. Compression codes…
As we continue to find applications where the currently available noisy devices exhibit an advantage over their classical counterparts, the efficient use of quantum resources is highly desirable. The notion of quantum autoencoders was…
The dynamical-algebraic structure underlying all the schemes for quantum information stabilization is argued to be fully contained in the reducibility of the operator algebra describing the interaction with the environment of the coding…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
The problem of classical data compression when the decoder has quantum side information at his disposal is considered. This is a quantum generalization of the classical Slepian-Wolf theorem. The optimal compression rate is found to be…
Recent advancements in quantum computing highlight the need for efficient encoding of classical data into quantum states to ensure robust quantum information processing. Traditional encoding schemes often impose impractical requirements…
Quantum direct coding or Schumacher compression generalised the ideas of Shannon theory, gave an operational meaning to the von Neumann entropy and established the term qubit. But remembering that information processing is carried out by…
We study source compression with a helper in the fully quantum regime, extending our earlier result on classical source compression with a quantum helper [arXiv:1501.04366, 2015]. We characterise the quantum resources involved in this…
Over decades traditional information theory of source and channel coding advances toward learning and effective extraction of information from data. We propose to go one step further and offer a theoretical foundation for learning classical…
We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length…
The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical…
This thesis addresses problems in the field of quantum information theory. The first part of the thesis is opened with concrete definitions of general quantum source models and their compression, and each subsequent chapter addresses the…
Data compression can be achieved by reducing the dimensionality of high-dimensional but approximately low-rank datasets, which may in fact be described by the variation of a much smaller number of parameters. It often serves as a…