相关论文: Quantum relative entropy: general convergence crit…

A criterion of local continuity of the relative entropy of resource -- the relative entropy distance to the set of free states -- is obtained. Several basic corollaries of this criterion are presented. Applications to the relative entropy…

We show that a positive linear map preserves local continuity (convergence) of the entropy if and only if it preserves finiteness of the entropy, i.e. transforms operators with finite entropy to operators with finite entropy. The last…

We describe a generalized version of the result called quantum Dini lemma that was used previously for analysis of local continuity of basic correlation and entanglement measures. The generalization consists in considering sequences of…

The quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this paper we study the relation between this measure and a number of other measures used for that purpose,…

Uncertainty principle, a fundamental principle in quantum physics, has been studied intensively via various uncertainty inequalities. Here we derive an uncertainty equality in terms of linear entropy, and show that the sum of uncertainty in…

We prove that the quantum relative entropy decreases monotonically under the application of any positive trace-preserving linear map, for underlying separable Hilbert spaces. This answers in the affirmative a natural question that has been…

Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…

Continuity properties of the output entropy of positive linear maps between Banach spaces of trace class operators are investigated with the special attention to the classes of quantum channels and operations. It is shown that finiteness of…

Various measures have been suggested recently for quantifying the coherence of a quantum state with respect to a given basis. We first use two of these, the l_1-norm and relative entropy measures, to investigate tradeoffs between the…

We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…

Fidelity and relative entropy are two significant quantities in quantum information theory. We study the quantum fidelity and relative entropy under unitary orbits. The maximal and minimal quantum fidelity and relative entropy between two…

Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy…

Quantum coherence, incompatibility, and quantum correlations are fundamental features of quantum physics. A unified view of those features is crucial for revealing quantitatively their intrinsic connections. We define the relative quantum…

A physical system is in local equilibrium if it cannot be distinguished from a global equilibrium by ``infinitesimally localized measurements''. This should be a natural characterization of local equilibrium, but the problem is to give a…

Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…

An analogue of the mixing property of quantum entropy is derived for quantum relative entropy.It is applied to the final state of ideal measurement and to the spectral form of the second density operator. Three cases of states on a directed…

Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative $q$-entropy is generally unbounded for $q>1$. Upper bounds on the quantum relative $q$-entropy in terms…

In [1], Collins et al. showed that the quantum entropy of random graph states satisfies the so-called area law as the local dimension tends to be large. In this paper, we continue to study the fluctuation of the convergence and thus prove…

In this paper we deal with two quantum relative entropy preserver problems on the cones of positive (either positive definite or positive semidefinite) operators. The first one is related to a quantum R\'enyi relative entropy like quantity…

It is known that a necessary and sufficient condition for equality in the data processing inequality (DPI) for the quantum relative entropy is the existence of a recovery map. We show that equality in DPI for a sandwiched R\'enyi relative…