Related papers: Bounding generalized relative entropies: Nonasympt…
Currently, 'time' does not play any essential role in quantum information theory. In this sense, quantum information theory is underdeveloped similarly to how quantum physics was underdeveloped before Erwin Schrodinger introduced his famous…
Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the R\'enyi entropies is expected to enhance their scope in…
Inspired by works on information transmission through quantum channels, we propose the use of a couple of mutual entropies to quantify the efficiency of continual measurement schemes in extracting information on the measured quantum system.…
We introduce a simplified version of Connes-Narnhofer-Thirring's quantum dynamical entropy for quantum systems. It quantifies the amount of information gained about the initial condition from continuously monitoring an observable. A nonzero…
The quantum relative entropy $S(\rho||\sigma)$ is a widely used dissimilarity measure between quantum states, but it has the peculiarity of being asymmetric in its arguments. We quantify the amount of asymmetry by providing a sharp upper…
In this paper we give a self contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation etc. and their…
An axiomatic foundation regarding the entropy for complex systems is established. Missing from decades of research was the requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution,…
Tsallis entropy is a useful one-parameter generalization of the standard von Neumann entropy in information theory. We study the variance of Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact…
In this article, we review a general theoretical framework of thermodynamics of information on the basis of Bayesian networks. This framework can describe a broad class of nonequilibrium dynamics of multiple interacting systems with complex…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…
The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The…
Quantum information processing and computing tasks can be understood as quantum networks, comprising quantum states and channels and possible physical transformations on them. It is hence pertinent to estimate the change in informational…
The total entropy production quantifies the extent of irreversibility in thermodynamic systems, which is nonnegative for any feasible dynamics. When additional information such as the initial and final states or moments of an observable is…
The fundamental goal of information theory is to characterize complex operational tasks using efficiently computable information quantities, Shannon's capacity formula being the prime example of this. However, many tasks in quantum…
In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is…
The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…
The tight, in a sense, lower estimates of diamond-norm distance from a given quantum channel to the sets of degradable, antidegradable and entanglement-breaking channels are obtained via the tight continuity bounds for quantum mutual…
The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be…
Quantum capacities are fundamental quantities that are notoriously hard to compute and can exhibit surprising properties such as superadditivity. Thus, a vast amount of literature is devoted to finding tight and computable bounds on these…
In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the…