Related papers: Smooth Renyi Entropies and the Quantum Information…
In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy…
We address the problem of quantifying the information content of a source for an arbitrary information theory, where the information content is defined in terms of the asymptotic achievable compression rate. The functions that solve this…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic…
Bounds on information combining are a fundamental tool in coding theory, in particular when analyzing polar codes and belief propagation. They usually bound the evolution of random variables with respect to their Shannon entropy. In recent…
In the first part of this thesis, we discuss the algebraic approach to classical and quantum physics and develop information theoretic concepts within this setup. In the second part, we discuss the uncertainty principle in quantum…
After Shannon, entropy becomes a fundamental quantity to describe not only uncertainity or chaos of a system but also information carried by the system. Shannon's important discovery is to give a mathematical expression of the mutual…
We addressed the question of optimality of private quantum channels. We have shown that the Shannon entropy of the classical key necessary to securely transfer the quantum information is lower bounded by the entropy exchange of the private…
Quantum Shannon theory is loosely defined as a collection of coding theorems, such as classical and quantum source compression, noisy channel coding theorems, entanglement distillation, etc., which characterize asymptotic properties of…
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide…
We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the…
Statements of Shannon's Noiseless Coding Theorem by various authors, including the original, are reviewed and clarified. Traditional statements of the theorem are often unclear as to when it applies. A new notation is introduced and the…
Quantum information theory, particularly its entropic formulations, has made remarkable strides in characterizing quantum systems and tasks. However, a critical dimension remains underexplored: computational efficiency. While classical…
Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
Near-term quantum devices with limited qubits motivate the study of space-bounded quantum computation in the data stream model. We show that Shannon entropy estimation exhibits an exponential separation between quantum and classical space…
A novel definition of the conditional smooth Renyi entropy, which is different from that of Renner and Wolf, is introduced. It is shown that our definition of the conditional smooth Renyi entropy is appropriate to give lower and upper…
In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number…