Related papers: The Quantum Relative Entropy as a Rate Function an…
The R{\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital…
This paper considers links between the original risk-sensitive performance criterion for quantum control systems and its recent quadratic-exponential counterpart. We discuss a connection between the minimization of these cost functionals…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…
The uncertainty principle is one of the comprehensive and fundamental concept in quantum theory. This principle states that it is not possible to simultaneously measure two incompatible observatories with high accuracy. Uncertainty…
In sharp contrast to the corresponding classical systems cases it is not yet understood how to define a mechanical quantity with the interpretation of entropy creation rate for nonequilibrum stationary states of finite quantum systems with…
The quantum Renyi relative entropies play a prominent role in quantum information theory, finding applications in characterizing error exponents and strong converse exponents for quantum hypothesis testing and quantum communication theory.…
Resource identification and quantification is an essential element of both classical and quantum information theory. Entanglement is one of these resources, arising when quantum communication and nonlocal operations are expensive to…
In recent years it was recognized that properties of physical systems such as entanglement, athermality, and asymmetry, can be viewed as resources for important tasks in quantum information, thermodynamics, and other areas of physics. This…
The quantum relative entropy is frequently used as a distance measure between two quantum states, and inequalities relating it to other distance measures are important mathematical tools in many areas of quantum information theory. We have…
In this work, we introduce a notion of reachability entropy to characterize the smallest data rate which is sufficient enough to enforce reach-while-stay specification. We also define data rates of coder-controllers that can enforce this…
The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional…
We study the fundamental properties of the quantum f-relative entropy, where f(.) is an operator convex function. We give the equality conditions under monotonicity and joint convexity, and these conditions are more general than, since they…
Given two pairs of quantum states, a fundamental question in the resource theory of asymmetric distinguishability is to determine whether there exists a quantum channel converting one pair to the other. In this work, we reframe this…
The study of quantum correlations in High-dimensional bipartite systems is crucial for the development of quantum computing. We propose relative entropy as a distance measure of correlations may be measured by means of the distance from the…
For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one…
In quantum systems, entropy production is typically defined as the quantum relative entropy between two states. This definition provides an upper bound for any flux (of particles, energy, entropy, etc.) of bounded observables, which proves…
The entropic formulation of the inertia and the gravity relies on quantum, geometrical and informational arguments. The fact that the results are completly classical is missleading. In this paper we argue that the entropic formulation…
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state. The second one is based on the relative entropy…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…