Related papers: Trade--off relations for operation entropy of comp…
A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms.…
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…
The second law of thermodynamics can be expressed in terms of entropy production, which can be used to quantify the degree of irreversibility of a process. In this Chapter, we consider the standard scenario of open quantum systems, where a…
We establish the general framework of quantum fluctuation theorems by finding the symmetry between the forward and backward transitions of any given quantum channel. The Petz recovery map is adopted as the reverse quantum channel, and the…
Bipartite entanglement in the ground state of a chain of $N$ quantum spins can be quantified either by computing pairwise concurrence or by dividing the chain into two complementary subsystems. In the latter case the smaller subsystem is…
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…
Quantum entropies and state distances are analyzed in polaronic systems with short range (Holstein model) and long range (Fr$\ddot{o}$hlich model) electron-phonon coupling. These quantities are extracted by a variational wave function which…
Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…
In quantum information theory, communication capacities are mostly given in terms of entropic formulas. Continuity of such entropic quantities are significant, as they ensure uniformity of measures against perturbations of quantum states.…
A way to construct Boltzmann entropy, i.e., the entropy as a function of a microscopic pure state, for quantum field systems is proposed. Operators that shift the field in wavevector space are used in the construction. By employing an…
For all p > 1, we demonstrate the existence of quantum channels with non-multiplicative maximal output p-norms. Equivalently, for all p >1, the minimum output Renyi entropy of order p of a quantum channel is not additive. The violations…
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 entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…
Relations between Shannon entropy and Renyi entropies of integer order are discussed. For any N-point discrete probability distribution for which the Renyi entropies of order two and three are known, we provide an lower and an upper bound…
In this work, we use the theory of quantum states over time to define an entropy $S(\rho,\mathcal{E})$ associated with quantum processes $(\rho,\mathcal{E})$, where $\rho$ is a state and $\mathcal{E}$ is a quantum channel responsible for…
This paper introduces a method for calculating the quantum relative entropy of channels, an essential quantity in quantum channel discrimination and resource theories of quantum channels. By building on recent developments in the…
Given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the "partial information" one system needs conditioned…
Quantum entanglements, describing truly quantum couplings, are stu died and classified from the point of view of quantum compound states. We show that c lassical-quantum correspondences such as quantum encodings can be treated as…
We study the entanglement of a pure state of a composite quantum system consisting of several subsystems with $d$ levels each. It can be described by the R\'enyi-Ingarden-Urbanik entropy $S_q$ of a decomposition of the state in a product…
We establish a tight upper bound for the difference in von Neumann entropies between two quantum states, $\rho_1$ and $\rho_2$. This bound is expressed in terms of the von Neumann entropies of the mutually orthogonal states derived from the…