Related papers: Strong Subadditivity Lower Bound and Quantum Chann…

The mathematical structure of quantum entanglement is studied and classified from the point of view of quantum compound states. We show that t he classical-quantum correspondences such as encodings can be treated as dia gonal (d-)…

We investigate the relation between the scaling of block entropies and the efficient simulability by Matrix Product States (MPS), and clarify the connection both for von Neumann and Renyi entropies (see Table I). Most notably, even states…

We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…

Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a…

We show that the density-matrix states of noncomposite qudit systems satisfy entropic and information relations like the subadditivity condition, strong subadditivity condition, and Araki--Lieb inequality, which characterize hidden quantum…

Theoretical understanding of the scaling of entropies and the mutual information has led to significant advances in the research of correlated states of matter, quantum field theory, and gravity. Measuring von Neumann entropy in quantum…

In this Letter, two counterexamples show that the superadditivity inequality of relative entropy is not true even for the full-ranked quantum states. Thus, an inequality of quantum channels and complementary channels is not also true.…

Capacities of quantum channels are fundamental quantities in the theory of quantum information. A desirable property is the additivity for a capacity. However, this cannot be achieved for a few quantities that have been established as…

We report lowest-order series expansions for primary matrix functions of quantum states based on a perturbation theory for functions of linear operators. Our theory enables efficient computation of functions of perturbed quantum states that…

This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…

Coherent information is a useful concept in quantum information theory. It connects with other notions in data processing. In this short remark, we discuss the coherent information saturating its upper bound. A necessary and sufficient…

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…

The von Neumann entanglement entropy is a useful measure to characterize a quantum phase transition. We investigate the non-analyticity of this entropy at disorder-dominated quantum phase transitions in non-interacting electronic systems.…

We study the von Neumann entropy of the partial trace of a system of two two-level atoms (qubits) in a dispersive cavity where the atoms are interacting collectively with a single mode electromagnetic field in the cavity. We make a contrast…

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 entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one…

We consider families of tight upper bounds on the difference $S(\rho)-S(\sigma)$ with the rank/energy constraint imposed on the state $\rho$ which are valid provided that the state $\rho$ partially majorizes the state $\sigma$ and is close…

Pedagogical introduction into the problem of the mathematical description of the quantum correlation (entanglement) of composite quantum systems is represented. The notion is substantiated about the fact that the conventional algorithm of…

Quantum networks play a key role in many scenarios of quantum information theory. Here we consider the quantum causal networks in the manner of entropy. First we present a revised smooth max-relative entropy of quantum combs, then we…

The information content of continuous quantum variables systems is usually studied using a number of well known approximation methods. The approximations are made to obtain the spectrum, eigenfunctions or the reduced density matrices that…