Related papers: Continuity of the von Neumann entropy
We axiomatically characterize the Tsallis entropy of a finite quantum system. In addition, we derive a continuity property of Tsallis entropy. This gives a generalization of the Fannes inequality.
We investigate entropy transport for universal scaling phenomena in closed quantum many-body systems far from equilibrium. From spatially resolved experimental data of a spinor Bose gas, we demonstrate that entropy decreases on…
We develop a quantum relative entropy method for the mean-field limit of quantum many-body systems. For closed systems governed by the von Neumann equation, we prove a quantitative stability estimate between the $N$-body density matrix and…
We derive the monotonicity of the quantum relative entropy by an elementary operational argument based on Stein's lemma in quantum hypothesis testing. For the latter we present an elementary and short proof that requires the law of large…
We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we…
We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched…
We obtain some results of existence and continuity of physical measures through equilibrium states and apply these to non-uniformly expanding transformations on compact manifolds with non-flat critical sets, obtaining sufficient conditions…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…
We analyze, for a general concave entropic form, the associated conditional entropy of a quantum system A+B, obtained as a result of a local measurement on one of the systems (B). This quantity is a measure of the average mixedness of A…
We describe an efficient theoretical criterion, suitable for indistinguishable particles to quantify the quantum correlations of any pure two-fermion state, based on the Slater rank concept. It represents the natural generalization of the…
Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the…
To find the essential nature of quantum theory has been an important problem for not only theoretical interest but also applications to quantum technologies. In those studies on quantum foundations, the notion of uncertainty plays a primary…
We propose a nonextensive generalization (q parametrized) of the von Neumann equation for the density operator. Our model naturally leads to the phenomenon of decoherence, and unitary evolution is recovered in the limit of q -> 1. The…
The measurement-based feedback (MBF) control offers several powerful means for preparing the desired target quantum state. Therefore, it is important to investigate fundamental properties of MBF. In particular, how the entropy of the…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
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…
We investigate entropy minimization problems for quantum states subject to convex block-separable constraints. Our principal result is a quantitative stability theorem: under a natural confining (fixed-support) hypothesis, if a state has…
Structure in quantum entanglement entropy is often leveraged to focus on a small corner of the exponentially large Hilbert space and efficiently parameterize the problem of finding ground states. A typical example is the use of matrix…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
We discuss some general properties of the symmetry-resolved von-Neumann entanglement entropy in systems with particle number conservation and describe how to obtain the entanglement components from correlation functions for Gaussian…