Related papers: Reverse Test and Characterization of Quantum Relat…
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…
The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of…
We study a variant of quantum hypothesis testing wherein an additional 'inconclusive' measurement outcome is added, allowing one to abstain from attempting to discriminate the hypotheses. The error probabilities are then conditioned on a…
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…
The most fundamental properties of quantum entropy are derived by considering the union of two ensembles. We discuss the limits these properties put on an entropy measure and obtain that they uniquely determine the form of the entropy…
We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the specified error…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
In this article, we generalize a proof technique by Alicki, Fannes and Winter and introduce a method to prove continuity bounds for entropic quantities derived from different quantum relative entropies. For the Umegaki relative entropy, we…
For a special class of bipartite states we calculate explicitly the asymptotic relative entropy of entanglement $E_R^\infty$ with respect to states having a positive partial transpose (PPT). This quantity is an upper bound to distillable…
The resource theory of asymmetry is a framework for classifying and quantifying the symmetry-breaking properties of both states and operations relative to a given symmetry. In the special case where the symmetry is the set of translations…
The data processing inequality states that the quantum relative entropy between two states $\rho$ and $\sigma$ can never increase by applying the same quantum channel $\mathcal{N}$ to both states. This inequality can be strengthened with a…
In this paper, we introduce the resource theory of unextendibility as a relaxation of the resource theory of entanglement. The free states in this resource theory are the k-extendible states, associated with the inability to extend quantum…
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…
The example provided in the comment [arXiv:0803.2241] concerns a situation where the system is initially at negative temperature. It is known that in such cases the Law of Entropy Decrease holds. Nevertheless, this does not challenge the…
We consider thermal relaxation process of a quantum system attached to a single or multiple reservoirs. Quantifying the degree of irreversibility by entropy production, we prove that the irreversibility of the thermal relaxation is…
Entanglement entropies calculated in the framework of quantum field theory on classical, flat or curved, spacetimes are known to show an intriguing area law in four dimensions, but they are also notorious for their quadratic ultraviolet…
We introduce a framework to study discrete-variable (DV) quantum systems based on qudits. It relies on notions of a mean state (MS), a minimal stabilizer-projection state (MSPS), and a new convolution. Some interesting consequences are: The…
The nonadiabatic entropy production is a useful tool for the thermodynamic analysis of continuously dissipating, nonequilibrium steady states. For open quantum systems, two seemingly distinct definitions for the nonadiabatic entropy…
An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…
A novel theoretical framework, the inverse problem approach, is proposed to calculate non-perturbative quantities in quantum chromodynamics (QCD). Based on the dispersion relation of quantum field theory, this approach determines unknown…